Class 11 Commerce Applied Mathematics - Descriptive Statistics

The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it.
English
Hindi Maths
Science
Social Studies
$85$
$60$
$35$
$50$
$70$

Draw a bar-graph (chart) to represent the following data:
Name of the animals
Goat
Horse
Cow
Camel
Elephant
Age (in years)
$12$
$15$
$15$
$26$
$60$

Find the quartile deviation of 6, 12,14, 16, 18, 20 and 24.

The ascending order of the given observations is 6, 12, 14, 16, 18, 20, 24

$Q_1\, =\, \left ( \displaystyle \frac{n\, +\, 1}{4} \right )^{th}$ observation = 2nd observation = 12

$Q_3\, =3\, \left ( \displaystyle \frac{n\, +\, 1}{4} \right )^{th}$ observation = 6 th observation = 20

$Q.D.\, =\, \displaystyle \frac{Q_3\, -\, Q_1}{2}\, =\, \displaystyle \frac{20\, -\, 12}{2}\, =\, 4$

Months Jan Feb Mar Apr May Jun Jul
Number of
sandwiches sold 12 23 15 10 25 16 22
Draw the line graph for the following data.

The following line graph shows the yearly sales figures for a manufacturing company.
(a) What were the sales in (i) $2002$ (ii) $2006$ ?
(b) What were the sales in (i) $2003$ (ii) $2005$ ?
(c) Compute the difference between the sales in $2002$ and $2006$ .
(d) In which year was there the greatest difference between the sales as compared to its previous year?

a) In

$2002$ , it was Rs

$4$ crores and in

$2006$ , it went to Rs

$8$ crores

b) In

$2003$ , sales was Rs.

$7$ crores and in

$2005$ , it was Rs

$10$ crores

c) Difference in sales between

$2002$ and

$2006$ is Rs

$4$ crores

$2005$

Write the coordinates of the vertices of each of these adjoining figures.

For the rectangle :

$A(2,0)$ ;

$B(0,0)$ ;

$C (0,3)$ ;

$D (2,3)$

For the parallelogram PQRS:

$P(4,3)$ ;

$Q (6,1)$ ;

$R (6,5)$ ;

$S(4,7)$

For the triangle KLM :

$K(10,5)$ ;

$L (7,7)$ ;

$M (10,8)$

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
Political Party A B C D E F
Seats Won 75 55 37 29 10 37
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?

(i) Bar graph

ii) Party

$A.$

Identify the scale used on the axes of the adjacent graph. Write the frequency distribution from it

Scale : on X-axis

$= 1\ cm. = 1$ class interval
on X-axis

$= 1\ cm. = 10$ number of students

Class	I	II	III	IV	V	VI
No. of students $(f)$	$40$	$55$	$65$	$50$	$30$	$15$

Find the median and quartile deviation for the following data.
$x$ $3$ $4$ $5$ $6$ $7$
$f$ $12$ $35$ $52$ $41$ $18$

Let us find the cumulative frequency for the given data.

$x$	$f$	Cumulative frequency $f_{c}$	Remarks
$3$	$12$	$12$	$12$ , the first $12$ scores correspond to $x = 3$
$4$	$35$	$47$	$(12 + 35)$ from $13^{th}$ to $47^{th}$ scores correspond to $x = 4$
$5$	$52$	$99$	$(47 + 52)$ from $48^{th}$ to $99^{th}$ scores correspond to $x = 5$
$6$	$41$	$140$	$(99 + 41)$ from $100^{th}$ to $140^{th}$ scores correspond to $x = 6$
$7$	$18$	$158$	$(140 + 18)$ from $141^{st}$ to $158^{th}$ scores correspond to $x = 7$ .

Observe that

$n = 158$ , the last cumulative frequency.

$Median = \dfrac {n + 1}{2}th\ score = \dfrac {158 + 1}{2}th\ score = 79.5^{th}\ score \approx 80^{th}$ score.
From the column

$f_{c}$ , from

$48^{th}$ to

$99^{th}$ score corresponds to

$x = 5$ . Hence,

$80^{th}$ position

$= 5$ . Therefore,

$median = 5$ .

The marks scored by $6$ students in a preparatory exam are given here:
$56, 71, 49, 90,88$ .
Find the median score and semi-quartile range

Arranging the scores in ascending order we get,

$49, 56, 71, 75, 88, 90$ .

$Median = \dfrac {6 + 1}{2}th\ score = 3.5th score$

$= 3^{rd} score + 0.5(4^{th} score - 3^{rd} score)$

$Median = 71 + 0.5(75 - 71) = 71 + 2 = 73\ marks$ .
To find semi-inter quartile range

$Q_{1} = \dfrac {6 + 1}{2}th\ score = 1.7^{th}\ score$

$= 1st score + 0.75 (2^{nd} score - 1^{st} score)$

$Q_{1} = 49 + 0.75 (56 - 59) = 49 + 0.75(7) = 49 + 5.25 = 54.25 \approx 54\ marks$ .

$Q_{3} = \dfrac {3(6 + 1)}{4}th\ score = 5.25^{th} score$

$= 5^{th} score + 0.25(6^{th}score - 5^{th} score)$

$Q_{3} = 88 + 0.25 (90 - 88) = 88 + 0.5 = 88.5 \approx 89$ .
Hence
semi-inter quartile range

$= \dfrac {Q_{3} - Q_{1}}{2} = \dfrac {89 - 54}{2} = \dfrac {35}{2} = 17.6\approx 18$ .

The coefficient of variations of two series are $58$ and $69$ . Their standard deviations are $21.2$ and $15.6$ . What are their arithmetic means?

We know that coefficient of variation, C.V.

$=\displaystyle\frac{\sigma}{\bar{x}}\times 100$ .

$\therefore \bar{x}=\displaystyle\frac{\sigma}{C.V}\times 100$ .

Mean of the first series,

$\bar{x_1}=\displaystyle\frac{\sigma}{C.V}\times 100$

$=\displaystyle\frac{21.2}{58}\times 100$

$\because C.V =58$ and

$\sigma =21.2$

$=\displaystyle\frac{2120}{58}=36.6$
Mean of the second series,

$\bar{x_2}=\displaystyle\frac{\sigma}{C.V}\times 100$

$=\displaystyle\frac{15.6}{69}\times 100$

$\because C.V =69$ and

$\sigma =15.6$

$=\displaystyle\frac{1560}{69}$

$=22.6$
A.M of the I series

$=36.6$ and the A.M of the II series

$=22.6$ .

If the point $(3, 4)$ lies on the graph of the equation $3y=ax+7$ , fine the values.

Solution:

Given

$3y=ax+7$

putting

$x=3$ and

$y=4$ .

$3(4)=a(3)+7$

$12=3a+7$

$3a=5$

$a=\dfrac{5}{3}$

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of children $135$ $120$ $95$ $100$ $90$ $80$
Answer the following question.
Find the ratio of students of class sixth to the students of class eight.

Number of children in

$6^{th}$ class is

$120$ and in

$8^{th}$ class is

$100$ . So, the ratio of students of class

$6^{th}$ to students of class

$8^{th}$ is :-

$=\dfrac{120}{100}$

$=\dfrac{12}{10}$

$= 12 : 10$

$= 6: 5$

1421142_1072763_ans_f82de48ceac14426b67a5510e5ef3ca6.png

Read the graph and answer the following questions.
How many buses are manufactured in the first $6$ months of the year?
What is the scale of the graph?
Is the number of bus manufacturing in the month of May $200$ more than the previous month?
Depict the information in a tabular form.
Now use the table form a pictograph.

$(1)$ Buses are manufactured in the first

$$6$$ months of the year

$=600+800+1000+1200+1400+1600+1800+1800=10,200$

$(2)$ The scale of the graph is

$1$ division

$=200$ buses

$(3)$ Yes.

$(4)$ Information in a tabular form is shown:

Month of the year	Number of buses manufactured
January	$600$
February	$800$
March	$1000$
April	$1200$
May	$1400$
June	$1600$
July	$1800$
August	$1800$

Let us represent

$200$ buses by the symbol of one bus as shown below.

We can represent number of buses horizontally and months vertically.(shown above)

1480446_1093115_ans_14b1dcb757594b8bacf21730d52df6ca.png

Draw a bar graph for the following data.
Population of India in successive census years:
Year 1941 1951 1961 1971 1981 1991 2001
Population 320 360 440 550 680 850 1000

The given above graph shown given data

Population of the India in successive census years.

1174405_1208881_ans_28c1c797cebd4d70b747c4e1d09cfdca.PNG

Match the values of $\varrho _{1},\varrho _{2},\varrho _{3}$ for the following data values
$13,14,7,12,17,8,10,6,15,18,21,20$

Ascending order of the data is,

$6, 7, 8, 10, 12, 13, 14, 15, 17, 18, 20, 21$

Here,

$n = 12$

$Q_1 = \dfrac{n}{4} ^{th}$ Observation

$= \dfrac{12}{4} = 3^{rd}$ observation

$= 8$

$Q_2 =$ Average of

$6 ^{th} , 7^{th}$ Observations

$= \dfrac{13+14}{2} = 13.5$

$Q_3 = \dfrac{3n}{4} ^{th}$ Observation

$= \dfrac{36}{4} = 9^{th}$ observation

$= 17$

When the scale along the x-axis does not start at the origin, we show it by a kink (break or a zig - zag curve of the origin). What is a kink? Why it is used?

A kink is a zig-zag line that is usually drawn in the

$x$ -axis near the origin when the scale on the axis does not start from zero. A kink denotes the missing divisions.

Draw a bar graph for the following data.
Population of India in successive census years.
Year $1941$ $1951$ $1961$ $1971$ $1981$ $1991$ $2001$
Population (in millions)(approx.) $320$ $360$ $440$ $550$ $680$ $850$ $1000$
Source: Data from census of India $1991$ and $2001$ .

$\Rightarrow$ The above bar graph shows population of India in successive census years.

$\Rightarrow$

$x-axis$ contains successive years.

$\Rightarrow$

$y-axis$ contains population (in millions)

1222632_1137583_ans_10f97bbaf49a444b838450e0d07b125c.jpeg

What percentage of the families have $4$ children ?

The percentage of families having

$4$ children

$=\dfrac{60}{300}\times 100 = 20\%$

The daily temperature recorded (in degree $F$ ) at a place during a week was as under:
Monday Tuesday Wednesday Thursday Friday Saturday
$35.5$ $30.8$ $27.3$ $32.1$ $23.8$ $29.9$

Calculate the mean temperature.

Sum of temperature during whole week

$= 35.5 + 30.8 + 27.3 + 32.1 + 23.8 + 29.9 =179.4$

Total number of days

$= 6$

Mean temperature

$=\dfrac{sum\,of\,temperature\,during \,whole\,week}{number\,of\,days}=\dfrac{179.4}{6}=29.9^{\circ}$ F

In what ways is the bar graph better than pictography.

Bar graph is better than pictograph in following ways-

Bar graph is better than a pictograph when the exact quantities of the commodities represented are to be known. In a pictograph, one needs to count all the symbols/icons and then multiply with the scale factor. Where as in a bar graph, one has to read the value written next to the bar.
Bar graphs use bars and numbers to show information, and pictographs use pictures to show information. With a pictograph you need to count each time to find how many, but with a bar graph you can just look at the number.

A number of children in six different classes are given below. Represent the data on the bar graph:

We can draw the bar graph by following the given steps:

Step

$1:$ On a graph paperdraw a horizontal line

$OX$ as

$x-$ axis and vertical line

$OY$ as

$y-$ axis.

Step

$2:$ Along

$OX,$ write the years at the points that are taken at a uniform gap.

Step

$3:$ Choose the scale

$1$ class

$=30$ students

Step

$4:$ Draw bars of equal width on the

$x-$ axis.The difference between the two bars should be the same.

We get the following bar graph:

1480531_1261351_ans_2f75e9fbd47c49f494bb3f23e5f53d36.png

In a survey of $300$ families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given:Read the graph carefully and answer the following questions:
How many family have no child?

$(ii)$ Zero.There is no bar which is at zero in the

$x-$ axis.

Whose savings in the month of April is the least?

1258621_1308866_ans_7e6c79e53fa142ce90afdb8d586c8791.jpeg

In a survey of $300$ families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given: Read the graph carefully and answer the following question: How many family have $2$ children each?

From the graph:

$(i) 60$ families have

$2$ children each.

Were the two plants of the same height during any week shown here? specify.

The height grown by plant

$A$ in

$1 \mathrm{st}$ week is

$2\ \mathrm{cm}$

The height grown by plant

$A$ in

$2 \mathrm{nd}$ week is

$8-2=6\ \mathrm{cm}$

The height grown by plant

$A$ in

$3 \mathrm{rd}$ week is

$10-8=2\ \mathrm{cm}$

The height grown by plant

$B$ in

$1 \mathrm{st}$ week is

$1\ \mathrm{cm}$

The height grown by plant

$B$ in

$2 \mathrm{nd}$ week is

$8-1=7\ \mathrm{cm}$

The height grown by plant

$B$ in

$3 \mathrm{rd}$ week is

$11-8=3\ \mathrm{cm}$

From the above data

$A$ and

$B$ does not grows same height

The number of books issued from a library in five days is given below. Represent the information in the form of a bar graph.

1281275_1377909_ans_2b625f25a6454766ad2d758ebf04b168.png

_______ displays data that changes continuously over periods of time.

Line graph displays data that changes continuously over periods of time.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did the person start from his home?

Observing the graph, we conclude that

At 10 AM, the person start from his home.

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.
On which day was the difference in temperatures the maximum for both the weeks?

$\text{friday}$ the difference in temperatures was the maximum for both the weeks.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did he cover $16$ km of his journey ?

Observing the graph, we conclude that,

He covered 16 km of his journey at 2 PM.

The graph given below gives the actual and expected sales of cars of a company for $6$ months. Study the graph and answer the questions that follow.
What are the average sales of cars in the last three months?

The average sale of the given months

$= \dfrac{125 + 100 + 150 } 3=\dfrac{375}3 = 125$

The graph given below gives the actual and expected sales of cars of a company for $6$ months. Study the graph and answer the questions that follow.
What was the total sale of cars in the months- Jan, Feb, and March?

The total sale for the given months

$=75 + 100 + 75 = 250$

The following table gives the growth chart of a child.
Draw a line graph for the table and answer the questions that follow.
How much taller was the child at the age of 10 than at the age of $6$ ?

Using the data given in the chart, the graph between height and age of a child is shown above.

From the graph, we can say that the child is

$110$ cm at the age of

$6$ years and

$130$ cm at the age of

$10$ years.

Hence, the child is of age

$10$ years is

$20$ cm taller than the child at the age of

$6$ years.

1884447_1794540_ans_88e541fb9f67412b95723691d8038f02.png

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
At what time is the temperature $3^{o}$ C?

From the graph, we can say that, at 6 AM the temperature is 3°C.

The following is the time-distance graph of Sneha's walking
Find her average speed in km/hour.

From the graph, we know that

Total distance travelled = 2 km

Total time taken = 55 min = 55/60 hr

Now, Average Speed = Total distance travelled / Total time taken = 2 x (60/55) km/hr = 2.18 km/hr

∴ Hence the average speed is 2.18 km/hr.

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
Which vendor has sold more ice cream on Friday?

From the graph, we can see that, Vendor A sold more ice creams than Vendor B on Friday.

The points on the graph below represent the height and weight of the donkey, dog, crocodile, and ostrich shown in the drawing.
What are the two variables represented in the graph?

The two variables represented in the graph are as follows:

Y-axis : Weight

X-axis : Height

Hence, Weight and Height are two variables.

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
On which day was the difference in sales the maximum?

From the graph, we can see that, the difference of sales is maximum on Thursday ( 20 ice cream ).

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did he return home ?

Observing the graph, we conclude that,

He returned home at 10 PM.

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
What is the temperature a t $8$ am?

$7 \circ C$

The shoppers who come to a departmental store are marked as: man $(M)$ , woman $(W)$ , boy $(B)$ or girl $(G)$ . The following list gives the shoppers who came during the first hour in the morning:
$W, W, W, G, B, W, W, M, G, G, M, M, W, W, W, W, G, B, M, W, B, G, G, M, W, W, M,$
$M,W,W,W,M,W, B, W, G, M, W, W, W, W, G, W, M, M, W, W, M, W, G, W, M, G,$
$W, M, M, B, G, G, W$
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Answer:-

Grouping like terms together

$W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,W,$

$M,M,M,M,M,M,M,M,M,M,M,M,M,M,M,B,B,B,B,B,G,G,G,G,G,G,G,G,G,G,G,G.$

Frequency Distribution Table:-

Shoppers	Tally Marks	Frequency
$W$		$28$
$M$		$15$
$B$		$5$
$G$		$12$

Bar Graph:- Attached Image

The number of days a hillside city received snow in different years.
Year $2003$ $2004$ $2005$ $2006$
Days $8$ $10$ $5$ $12$

$\Rightarrow$ We draw, years on

$x-axis$ and days on

$y-axis$ .

$\Rightarrow$ The above graph shows linear graph.

1109697_301810_ans_89519970a3fc41d696dc27f80e6a751a.jpeg

To get an interest of Rs. 280 per year,how much money should be deposited?

answer required

Given the marks scored by Rita's out of 100, in five subjects in a particular test.
Subject Marks
English 78
Hindi 72
Maths 96
Science 88
S.St 80
Can we draw the bar graph for above data?
If yes enter 1 else 0.

$\Rightarrow$ The above graph represent bar graph drawn from given frequency table.

$\therefore$ We can draw the graph from the given data.

$\therefore$ Answer is

$1$

1236103_302399_ans_41fc32a24b60451aa6c611489a374f35.jpeg

Following data gives total marks (out $600$ ) obtained by six children of a particular class. Represent the data on a bar graph.
Students Ajay Bali Dipti Faiyaz Geetika Hari
Marks
obtained $450$ $500$ $300$ $360$ $400$ $540$

To choose an appropriate scale we make equal divisions taking increments of

$50$ . Thus 1 unit will represent

$50$ marks,
1111488_403780_ans_145384f704d44feb92cde9f1c168900c.jpg

A survey conducted by an organisation for the cause of illness and death among the women between the ages $15-44$ (in years) worldwide, found the following figures (in %):
(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women's ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

(i) Bar graph

(ii) Major cause of women's ill health : Reproductive health conditions :

$31.8$ %

(iii) Factors are:
(i) Medical infrastructure in work.
(ii) Lack of treatment facilitators and facilities.

For an experiment in Botany two different plants, plant A and plant B were grown under similar laboratory conditions. The heights were measured at the end of each week for $3$ weeks. The results are shown by the following graph.
(a) How high was Plant A after (i) $2$ weeks (ii) $3$ weeks?
(b) How high was Plant B after (i) $2$ weeks (ii) $3$ weeks?
(c) How much did Plant A grow during the $3^{rd}$ week?
(d) How much did Plant B grow from the end of the $2nd$ week to the end of the $3rd$ week?
(e) During which week did plant A grow most?
(f) During which week did plant B grow least?
(g) Were the two plants of the same height during any week shown here? Specify.

In the graph

$x-$ axis represents weeks and

$y-$ axis represents the heights of the plant.

Scale :

$x-$ axis

$7$ cm

$= 1$ week

$y-$ axis

$1$ cm

$= 1$ cm in height

To find the height of plant at particular week:

Trace the vertical line parallel to

$y-$ axis passing from the point on

$x-$ axis, find the point where this vertical line intersects the graph.

Now from that point trace a horizontal line parallel to

$x-$ axis, this line intersects the

$y-$ axis at required point.

To find the week at particular height:

Trace the horizontal line parallel to

$x-$ axis passing from the height point on y-axis, find the point where this horizontal line intersects the graph.

Now from that point trace a vertical line parallel to

$y-$ axis, this line intersects the

$x-$ axis at required point.

Now,

a) Follow step 1 on graph for plant A at point i)

$2$ weeks and ii)

$3$ weeks, we get corresponding heights on

$y-$ axis,

$7$ cm for

$2$ weeks and

$9$ cm for

$3$ weeks.

b) Follow step 1 on graph for plant B at point i)

$2$ weeks and ii)

$3$ weeks, we get corresponding heights on

$y-$ axis,

$7$ cm for

$2$ weeks and

$10$ cm for

$3$ weeks.

c) To find grow during

$3^{rd}$ week, we have to find the height difference between

$2^{nd}$ and

$3^{rd}$ week, which is

$9$ cm

$- 7$ cm

$= 2$ cm

d) To find grow of plant B from end of

$2^{nd}$ week to end of

$3^{rd}$ week, we have to find height difference between

$3^{rd}$ and

$2^{nd}$ week,

$10$ cm

$- 7$ cm

$= 3$ cm

e) Find the grow of height level of plant A weekwise

$1^{st}$ week:

$1$ cm

$-0$ cm

$= 1$ cm

$2^{nd}$ week:

$7$ cm

$-1$ cm

$= 6$ cm

$3^{rd}$ week:

$9$ cm

$- 7$ cm

$= 2$ cm

so plant A grows on

$2^{nd}$ week the most

f) Find the grow of plant B week-wise

$1^{st}$ week:

$2$ cm

$-0$ cm

$= 2$ cm

$2^{nd}$ week:

$7$ cm

$-2$ cm

$= 5$ cm

$3^{rd}$ week:

$10$ cm

$- 7$ cm

$= 3$ cm

so plant B grow least on week

$1^{st}$

g) Graphs of plant A and plant B intersects at (

$2^{nd}$ week and

$7$ cm height), so plants were in same height which is

$7$ cm.

The following graph shows the temperature forecast and the actual temperature for each day of a week.
(a) On which day was the forecast temperature the same as the actual temperature?
(b) What was the maximum forecast temperature during the week?
(c) What was the minimum actual temperature during the week?
(d) On which day did the actual temperature differ the most from the forecast temperature?

We have two graphs actual and forecast, In the graph

$x-$ axis represents days and

$y-$ axis represents the temperature

Scale :

$x-$ axis

$4$ cm

$= 1$ day

$y-$ axis

$2$ cm

$= 5^0 C$

To find the temperature at particular day:

Trace the vertical line parallel to

$y-$ axis passing from the point on

$x-$ axis, find the point where this vertical line intersects the graph.

Now from that point trace a horizontal line parallel to

$x-$ axis, this line intersects the

$y-$ axis at required point.

To find the day at particular temperature:

Trace the horizontal line parallel to

$x-$ axis passing from the temperature point on

$y-$ axis, find the point where this horizontal line intersects the graph.

Now from that point trace a vertical line parallel to

$y-$ axis, this line intersects the

$x-$ axis at required point.

Now,

a) Forecast temperature and actual temperature are same where the graphs of both intersects which is Tuesday, Friday and Sunday

b) Follow step 1 to find temperature for graph forecast on days of week,

Mon

$- 15^0 C$

Tue

$- 20^0 C$

Wed

$- 25^0 C$

Thu

$- 22.5^0 C$

Fri

$- 15^0 C$

Sat

$- 30^0 C$

Sun

$- 35^0 C$

So, maximum forecast temperature during the week is

$35^0 C$

c) Follow step 1 to find temperature for actual graph on days of week

Mon

$-17.5^0 C$

Tue

$- 20^0 C$

Wed

$- 30^0 C$

Thu

$- 15^0 C$

Fri

$- 15^0 C$

Sat

$- 25^0 C$

Sun

$- 35^0 C$

So, minimum actual temperature during the week is

$15^0 C$

d) Difference between actual and forecast temperatures during the week

Mon,

$17.5-15= 2.5^0 C$

Tue,

$20 - 20 = 0^0 C$

Wed,

$30-25 = 5^0 C$

Thu,

$15 - 22.5 =-7.5^0 C$

Fri,

$15 - 15 = 0^0 C$

Sat,

$25- 30 =-5^0 C$

Sun,

$35 - 35 = 0^0C$

So, actual temperature differ most from forecast temperature is

$7.5^0 C$ which is on Thursday.

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

ST : Maximum girls :

$970$
Urban : Minimum girls :

$910$
Number of girls in rural

$>$ urban.

Draw a graph for the following.

i)
Side of square (in cm) 2 3 3.5 5 6
Perimeter (in cm) 8 12 14 20 24
Is it a linear graph?

(ii)
Side of square (in cm) 2 3 4 5 6
Perimeter (in cm) 4 9 16 25 36
Is it a linear graph?

(i) it is a linear graph as the line is a straight line.

(ii) It is not linear as the graph is a curve and is not a straight line.

The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W
W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

The following graph shows the temperature of a patient in a hospital, recorded every hour.
(a) What was the patient's temperature at $1\ \textbf{p.m.}$ ?
(b) When was the patient's temperature $38.5^{\circ} \textbf{C}$ ?
(c) The patient's temperature was the same two times during the period given.
What were these two times?
(d) What was the temperature at $1.30\ \textbf{p.m.}$ ? How did you arrive at your answer?
(e) During which periods did the patient's temperature showed an upward trend?

In the graph,

$x-$ axis represents the time and

$y-$ axis represents the temperature of the patient.

Scale :

$x-$ axis

$1$ cm

$= 1\ \text{hr}$

$y-$ axis

$1$ cm

$= 1\ ^\circ \text{C}$

Steps:

1) To find the temperature at particular time:

Trace the vertical line parallel to

$y-$ axis passing from the time point on

$x-$ axis, find the point where this vertical line intersects the graph.

Now from that point trace a horizontal line parallel to x-axis, this line intersects the

$y-$ axis at required point.

2) To find the time at particular temperature:

Trace the horizontal line parallel to

$x-$ axis passing from the temperature point on

$y-$ axis, find the point where this horizontal line intersects the graph.

Now from that point trace a vertical line parallel to

$y-$ axis, this line intersects the

$x-$ axis at required point.

Now,

a) Follow step 1 to find temperature corresponding to time

$1\ \text{pm}$ , you get point between

$36$ to

$37$ which is

$36.5^\circ \ \text{ C}$

b) Follow step 2 from point between

$38 -39$ i.e.

$38.5^\circ \ \text{C}$ , we get corresponding point on

$x-$ axis which is

$12$ noon.

c) In the graph we see

$36.5^0C$ is the temperature which is same. Follow step 2 to get corresponding times which is

$1^\circ$ and

$2\ \text{pm}$ .

d) temperature at

$1:30\ \text{pm}$ is

$36.5^0 C$ , since we know from (c) temperature is same between interval

$1\ \text{pm}$ to

$2\ \text{pm}$ .

e) To show upward trend graph continues with positive slope, we have

$9-10, 10-11$ , and

$2-3$ time interval where slope is positive. so patient's temperature showing upward trend in

$9-11\ \text{am}$ and

$2-3\ \text{pm}$ interval.

Use the tables below to draw linear graphs.
(a) The number of days a hill side city received snow in different years.
Year 2003 2004 2005 2006
Days 8 10 5 12

(b) Population (in thousands) of men and women in a village in different years.
Year 2003 2004 2005 2006 2007
Men in no. 12 12.5 13 13.2 13.5
Women in no. 11.3 11.9 13 13.6 12.8

Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples
Number of apples 1 2 3 4 5
Cost (in Rs.) 5 10 15 20 25
(b) Distance travelled by a car
Time (in hours) 6am 7am 8am 9am
Distance (in km) 40 80 120 160
(i) How much distance did the car cover during the period $7.30$ a.m. to $8$ a.m?
(ii) What was the time when the car had covered a distance of $100$ km since it's start?

(c) Interest on deposits for a year.
Deposit (in Rs.) 1000 2000 3000 4000 5000
Simple Interest (in Rs.) 80 160 240 320 400
(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on $Rs.2500$ for a year.
(iii) To get an interest of $Rs.280$ per year, how much money should be deposited?

b) i)

$20$ km

ii)

$7.30$ am

c) i) The graph is linear and it passes through the origin.

ii) Interest on Rs.

$2500$ is Rs.

$200$ .

iii) To get an interest of Rs.

$280$ per year, she must deposit Rs.

$3500$ .

A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.
(a) What is the scale taken for the time axis?
(b) How much time did the person take for the travel?
(c) How far is the place of the merchant from the town?
(d) Did the person stop on his way? Explain.
(e) During which period did he ride fastest?

In the graph

$x-$ axis represents the time period and

$y-$ axis represents the distance traveled by the courier person.

Scale :

$x-$ axis

$4$ cm

$= 1$ hr

$y-$ axis

$1$ cm

$= 2$ km

To find the distance at particular time:

Trace the vertical line parallel to y-axis passing from the time point on x-axis, find the point where this vertical line intersects the graph.

Now from that point trace a horizontal line parallel to x-axis, this line intersects the y-axis at required point.

To find the time at particular distance:

Trace the horizontal line parallel to x-axis passing from the distance point on y-axis, find the point where this horizontal line intersects the graph.

Now from that point trace a vertical line parallel to y-axis, this line intersects the x-axis at required point

Now,

$4$ cm

$= 1$ hr

b) Graph is starting from

$0$ km to

$22$ km, which means travelling distance is

$22$ km, so time taken is difference between time when person is on 0 km and when person is on

$22$ km, follow step 1 to find out time corresponding to distance, we get

$11:30 - 8= 3:30$ hr.

c) Since courier person is starting from

$0$ km and ending at

$22$ km, so the place of merchant is

$22$ km far from the town.

d) If we see the graph, there is a time interval from

$10:00$ am to

$10:30$ am when the distance covered is same i.e.

$16$ km, so yes the person did stop on his way.

e) We know that Speed

$=\dfrac{\text{Distance}}{\text{Time}}$

we have same time interval which is

$1$ hr, so speed is directly proportional to distance covered.

Distance covered in time interval

$8$ am to

$9$ am is more person ride fastest during

$8$ am to

$9$ am period.

The given graph represent the how much consumers would be willing to pay for store brand and brand name products. On average, how many more cents are consumers willing to pay for the brand name version of the product than the store brand version? (Round your answer to the nearest cent)

As we know,

$Average=\dfrac { \sum { (Price)\times (Responses) } }{ \sum { (Responses) } }$

Therefore, for store brand

$Average=\dfrac { \left( 5\times 68 \right) +\left( 6\times 56 \right) +\left( 7\times 48 \right) +\left( 8\times 32 \right) +\left( 9\times 30 \right) +\left( 14\times 10 \right) }{ \left( 68+56+48+32+30+14 \right) }$

$=$6.766$

$Average=\dfrac { \left( 5\times 85 \right) +\left( 6\times 79 \right) +\left( 7\times 64 \right) +\left( 8\times 55 \right) +\left( 9\times 42 \right) +\left( 10\times 27 \right) }{ \left( 85+79+64+55+42+27 \right) }$

$Average=\dfrac { 425+474+448+440+378+270 }{ 352 }$

$=$6.9176$

$Difference=$6.9176-$6.766$

$=$0.15$ or

$15$ cents

A scientist is doing study on person sleep. He classifies sleep activity in four stages: $1,2,3$ and $4$ . Stage $3$ is the only stage considered to be deep sleep.
Ajay goes to clinic for sleeping brainwashes analyzed. Doctor monitored the person's brainwashes in $15-$ minute intervals, for $8$ continuous hours, and categorized them into one of the four stages. The graph above shows this study.
Based on the graph, how many minutes did ajay spend in non-deep sleep over the course of the entire night?

Total number of

$15-$ minute interval in 8 hours

$=\dfrac{8\times 60}{15}=32$ .

Now from the graph, we can observe that Ajay achieves Stage

$3$ sleep

$12$ times in

$8$ hours.

Hence, the total number of times he was in non-deep sleep is

$32-12=20$ times.

Therefore, total time spent in non-deep sleep is

$20\times 15$ minutes

$=300$ minutes

Calculate quartile deviation for the following data:
$30, 18, 23, 15, 11, 29, 37, 42, 10, 21$

Arranged data is

$10,11,15,18,21,23,29,30,37,42$

$Q_1=$ Value of

$\left(\cfrac{n+1}{4}\right)^{th}$ term

$=2.75^{th}$ Term.

$Q_1=$

$2^{nd}$ term +

$0.75/(3^{rd}$ term-

$2^{nd}$ term)

$Q_1=$

$11+0.75(15-11)=14$

$Q_3=$ Value of

$\left(\cfrac{3(n+1)}{4}\right)^{th}$ term

$=8.25^{th}$ Term.

$Q_3=$

$30+0.25(37-30)=31.75$

$Q.D=\cfrac{Q_3-Q_1}{2}=\cfrac{31.75-14}{2}=8.875$

Calculate quartile deviation for the following data:
$3, 5, 8, 10, 12, 7, 5$

Arranged data is

$3,5,5,7,8,10,12$

$Q_1=$ Value of

$\left(\cfrac{n+1}{4}\right)^{th}$ term

$=2^{nd}$ term

$=5$

$Q_3=$ Value of

$\left(\cfrac{3n+3}{4}\right)^{th}$ term

$=6^{th}$ Term

$=10$

$Q.D=\cfrac{Q_3-Q_1}{2}=2.5$

Compute quartile deviation for each of the following tables.
Class interval frequency
$1 - 9$ $4$
$10 - 19$ $3$
$20 - 29$ $20$
$30 - 39$ $12$
$40 - 49$ $5$
$50 - 59$ $8$
$60 - 69$ $14$
$70 - 79$ $27$
$80 - 89$ $2$
$90 - 99$ $5$

Class Interval

Frequency

Cumulative Frequency

1-9

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

100

${ N }_{ 1 }$ for

${ Q }_{ 1 }=\cfrac { 100 }{ 4 } =25$

${ Q }_{ 1 }=L+\cfrac { N-{ C }_{ f } }{ f } \times i\\ \Rightarrow { Q }_{ 1 }=20+\cfrac { 25-27 }{ 20 } \times 10\\ \Rightarrow { Q }_{ 1 }=0.5+20-1=18.5$

${ N }_{ 3 }$ for

${ Q }_{ 3 }=\cfrac { 3N }{ 4 } =75$

$\Rightarrow { Q }_{ 3 }=69.5+\cfrac { 75-93 }{ 70 } \times 10\\ \Rightarrow { Q }_{ 3 }=66.92$

Therefore,

$\cfrac { { Q }_{ 3 }-{ Q }_{ 1 } }{ 2 } =\cfrac { 66.92-18.5 }{ 2 } =24.21.$

Calculate quartile deviation for the following data:
Age $3$ $6$ $9$ $12$ $15$
No. of children $4$ $8$ $11$ $7$ $12$

Age	3	6	9	12	15
Frequency	4	8	11	7	12
CF	4	12	23	30	42

$Q_1=$ Value of $\left(\cfrac{n+1}{4}\right)^{th}$ term $=10.75^{nd}$ term $=6$

$Q_3=$ Value of $\left(\cfrac{3n+3}{4}\right)^{th}$ term $=32.25^{th}$ Term $=15$

$Q.D=\cfrac{Q_3-Q_1}{2}=\cfrac{15-6}{5}=4.5$

Compute quartile deviation for each of the following tables.
Class interval frequency
$5 - 15$ $11$
$15 - 25$ $5$
$25 - 35$ $15$
$35 - 45$ $9$
$45 - 55$ $22$
$55 - 65$ $8$
$67 - 75$ $17$

Class Interval

Frequency

Cumulative Frequency

5-15

15-25

25-35

35-45

45-55

55-65

65-75

$\sum { f=87 }$

${ N }_{ 3 }$ for

${ Q }_{ 3 }=\cfrac { 3N }{ 4 } =\cfrac { 3\times87 }{ 4 } =65.25.$

$Q_1=\dfrac{n+1}{4}^{th} term$

$Q_3=\dfrac{3(n+1)}{4}^{th} term$

${ Q }_{ 3 }=65+\cfrac { 65.25-87 }{ 17 } \times 10=52.205.$

${ Q }_{ 1 }=h+\cfrac { N-{ C }_{ f } }{ f } \times I$

${ N }_{ 1 }$ for

${ Q }_{ 1 }=\cfrac { 87 }{ 4 } =21.75$

Therefore,

${ Q }_{ 1 }=15+\cfrac { 21.75-16 }{ 5 } \times 10\\ \Rightarrow { Q }_{ 1 }=15+11.5=26.5$

Therefore, Quartile deviation

$= \cfrac { 52.205-26.5 }{ 2 } =12.853.$

Calculate quartile deviation for the following data:
Marks scored $10$ $20$ $30$ $40$ $50$ $60$
No. of students $12$ $7$ $16$ $8$ $18$ $22$

Age	10	20	30	4	50	60
Frequency	12	7	16	8	18	22
CF	12	19	35	43	61	83

$Q_1=$ Value of $\left(\cfrac{n+1}{4}\right)^{th}$ term $=21^{nd}$ term $=30$

$Q_3=$ Value of $3\left(\cfrac{n+1}{4}\right)^{th}$ term $=63^{th}$ Term $=60$

$Q.D=\cfrac{Q_3-Q_1}{2}=\cfrac{60-30}{2}=15$

Calculate the quartile deviation for the following:
$C.I.$ $0-9$ $10-19$ $20-29$ $30-39$ $40-49$ $50-59$ $60-69$
$f$ $8$ $16$ $17$ $34$ $10$ $5$ $10$

We observe that the class intervals are in inclusive form. We have to convert them into exclusive form by adding the correction factor. You have learnt to add the correction factor in

$8^{th}$ standard.

Class interval	$f$	$f_{c}$
$-0.5 - 9.5$	$8$	$8$
$9.5 - 19.5$	$16$	$24$
$19.5 - 29.5$	$17$	$41$	$Q_{1} Class$
$29.5 - 39.5$	$34$	$75$	$Q_{3} Class$
$39.5 - 49.5$	$10$	$85$
$49.5 - 59.5$	$5$	$90$
$59.5 - 69.5$	$10$	$100$

To find

$Q_{1}$ :
Here

$N = 100$ . Hence

$N/4 = 25$ and

$25$ in

$f_{c}$ column corresponds to

$CI\ 19.5 - 29.65$ .
Hence

$LRL = 19.5, f_{c} = 24, f_{m} = 17$ and

$i = 10$ .
Thus we have

$Q_{1} = LRL + \left (\dfrac {\dfrac {N}{4} - f_{c}}{f_{m}}\right ) \times i = 19.5 + \left (\dfrac {25 - 24}{17}\right ) \times 10$

$= 19.5 + (0.058 \times 10) = 19.5 + 0.58 = 20.08$ .
To find

$Q_{3}$ :
We have

$3N/4 = (3\times 100)/4 = 75$ and

$75$ corresponds to

$CI\ 29.5 - 39.5$ in

$f_{c}$ column.
Thus

$LRL = 29.5, f_{c} = 41, f_{m} = 34$ and

$i = 10$ .
Therefore

$Q_{3} = LRL + \left (\dfrac {\dfrac {3N}{4} - f_{c}}{f_{m}}\right )\times i = 29.5 + \left (\dfrac {75 - 41}{34}\right ) \times 10$

$= 29.5 + (1\times 10) = 29.5 + 10 = 39.5$ .
We now compute quartile deviation:
quartile deviation

$= \dfrac {Q_{3} - Q_{1}}{2} = \dfrac {39.5 - 20.08}{2} = \dfrac {19.42}{2} = 9.71$ .

The runs scored by a batsman in seven innings are $28, 60, 85, 58, 74, 20, 90$ . Find $Q_{1}, Q_{2}, Q_{3}$ and quartile deviation

Arranging the scores in ascending we get,

$20, 28, 58, 60, 74, 85, 90$ .
There are

$7$ scores and

$n = 7$ .
i) First quartile

$(Q_{1}) = \dfrac {n + 1}{4}th\ score = \dfrac {7 + 1}{4}th\ score = 2^{nd}\ score = 28$ .
ii) Median

$(Q_{2}) = \dfrac {n + 1}{2}th\ score = \dfrac {7 + 1}{2}th\ score = 4^{th} score = 60$ .
(iii) Third quartile

$(Q_{3}) = \dfrac {3(n + 1)}{4} = \dfrac {3(7 + 1)}{4}th\ score = 6^{th}\ score = 85$ .
(iv) Quartile deviation

$= \dfrac {Q_{3} - Q_{1}}{2} = \dfrac {85 - 28}{2} = 28.5\approx 29$ .

Define or explain the concepts:
Higher Order Table

A complex table summarizes the complicated information and presents them into two or more interrelated categories. For example, if there are two coordinate factors, the table is called a two-way table or bi-variate table; if the number of coordinate groups is three, it is a case of three-way tabulation, and if it is based on more than three coordinate groups, the table is known as higher order tabulation or a manifold tabulation.

Define or explain the concepts:
Complex table

The complex table defines a table of records containing multiple fields stored on the Agentry Client in a structured and searchable format. A complex table can contain large amounts of data with records numbering in the thousands.

Give Reason :

Manifold table can presents 2 or 3 characteristics.

complex table summarizes the complicated information and presents them into two or more interrelated categories. For example, if there are two coordinate factors, the table is called a two-way table or bi-variate table; if the number of coordinate groups is three, it is a case of three-way tabulation, and if it is based on more than three coordinate groups, the table is known as higher order tabulation or a manifold tabulation.

The main characteristics of the statistical table are:

It shows the probability distribution or the frequency distribution or any relevant parameter distribution in a simplified manner.
It represents the quantitative and qualitative attributes of the parameters.
It can represent the data based on different time periods.

What are the different types of tables?

Statistical tables can be classified under two general categories, namely, general tables and summary tables.

General tables contain a collection of detailed information including all that is relevant to the subject or theme. The main purpose of such tables is to present all the information available on a certain problem at one place for easy reference and they are usually placed in the appendices of reports.

Summary tables are designed to serve some specific purposes. They are smaller in size than general tables, emphasize on some aspect of data and are generally incorporated within the text. The summary tables are also called derivative tables because they are derived from the general tables. The information contained in the summary table aims at analysis and inference. Hence, they are also known as interpretative tables.

The statistical tables may further be classified into two broad classes namely simple tables and complex tables. A simple table summarizes information on a single characteristic and is also called a univariate table.

Define or explain the concepts:
Complex Table

Answer the Following :
What is a complex table?

Define or explain the concepts:
Tabulation

Tabulation :

It is the process of presenting data collected through survey, experiment or record in rows and columns so that it can more easily be understood and can be used for further statistical analysis.

Write Short Note on the following:

Types of Table

Statistical tables can be classified under two general categories, namely, general tables and summary tables.

Draw a graph for the data given in the table. Hence find the number of days taken by $12$ workers to complete the work ?
No. of works
$x$
3 4 6 8 9 16
No. of days
$y$ 96 72 48 36 32 18

We are going to draw frequency curve from given table in question.

$\Rightarrow$ Now, we have to find number of days taken by

$12$ workers to complete the work

$\Rightarrow$ On x- axis draw vertical line from

$12$ , the line touches curve at point

$M$ . then draw horizontal line from

$M$ toward

$y-axis$

$\Rightarrow$ The point at which horizontal line touches

$y-axis$ is the number of days required

$12$ workers to complete there work.

$\Rightarrow$ The line touches at point

$26$

$\therefore$ Number of days required

$12$ worker to complete the work

$=26\,days$

1242481_1039737_ans_ba65c5de980a4383bd3730e75a7cae3f.jpeg

Sita practiced piano for 2hrs everyday during the month of January. How many hrs did she practice in January? (Use bar model for solving the sum)

$2hrs$ everyday she practiced,

Thus total hours

$=2\times a_0$ of days in January

$=2\times 31=62 hrs.$

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of Children $135$ $120$ $95$ $100$ $90$ $80$
How would you choose a scale?

I will select each box as showing 20 students
1161663_1072754_ans_cf31e44bb3024f908242a097cce56057.png

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of Children $135$ $120$ $95$ $100$ $90$ $80$
Answer the following question.
Which class has the maximum number of children? And the minimum?

From the bar graph, the class with maximum number of children is

$5^{th}$ as it has the bar with maximum height and

$10^{th}$ has minimum number of children as it has bar with minimum height
1421145_1072759_ans_f7db5e9d39a34f0395317d5da7efafb2.png

Draw a pic chart for the following data.
Item of expenditure Food Health Cloting Education Savings
Amount spent in rupess $3750$ $1875$ $1875$ $1200$ $7500$

The central angle

$=\dfrac{component\,value}{sum\,of\,all\,components}\times {360}^{\circ}$

Total amount

$=3750+1875+1875+1200+7500=16,200$

Hence, the central angle for each activity will be calculated as follows

Item of expenditure	Amount in rupees	Central angle
Food	$3750$	$\dfrac{3750}{16200}\times{360}^{\circ}={83.3}^{\circ}$
Health	$1875$	$\dfrac{1875}{16200}\times{360}^{\circ}={41.6}^{\circ}$
Clothing	$1875$	$\dfrac{1875}{16200}\times{360}^{\circ}={41.6}^{\circ}$
Education	$1200$	$\dfrac{1200}{16200}\times{360}^{\circ}={26.6}^{\circ}$
Savings	$7500$	$\dfrac{7500}{16200}\times{360}^{\circ}={166.6}^{\circ}$

1480518_1088215_ans_df1a5f0d95144561a758f5352e9da78a.png

Draw a bar graph ..
The number of saplings planted by a former in five consecutive weeks are given below.

1211308_1180219_ans_b6b9cc5723b84e57af5e9398d712f64a.jpeg

How much more is the total saving of Savita than the total saving of Megha?

Total saving by Savita

$= 1000$

Total saving by Megha

$= 550$

Savita saves

$1000 - 550 = Rs. 450$ than Megha.

How much is the saving of Vaishali in the month of April?

The saving of Vaishali in the month of April

$= Rs. 600$

Month Sale (in Rs)
March 2000
April 2500
May 4500
June 3000
July 4000
August 3500
Daily sales (in Rs) of Sushil Enterprises from March to August are given below :
Draw a bar graph to depict the above data.

Daily sales (in

$Rs$ ) of sushil Enterprises.

1369132_1177401_ans_a8b11b6522a948768ffe0c54e0cd5c8a.png

How much is the total saving of Saroj in the months March and April?

The savings of Saroj in the month of March is

$Rs.\;800$ and in April it is

$Rs.\; 400$ .

So, the total savings of Saroj would be,

$\begin{array}{l}{\rm{Total\;Savings}} &= 800 + 400\\ &= 1200\end{array}$

The names and number of animals in a certain zoo are given below. use the data to make a bar graph. (Scale : on Y-axis, 1 cm =4 animals)
Animals Deer Tiger Monkey Rabbit Peacock
Number 20 4 12 16 8

1172166_1176176_ans_4fa6770a32fc4422865ededf33586536.jpg

What is the percentage increase of earning from Thursday to friday ?

Earning on Thursday

$=400$

Earning on Friday

$=650$

The percentage increase in earning is

$=\dfrac{Earning\;in\;Friday\;-\;Earning \;in\;Thursday }{Earning \;in\;Thursday}\times 100$

$=\dfrac{650-400}{400}\times 100$

$=\dfrac{250}{400}\times 100$

$=\dfrac{250}{4}$

$=62.5\%$

Hence, the answer is

$62.5\%.$

What can you say about the position of the points (1,2,),(1,3),(1,-4),(1,0) and (1,8) locate on graph sheet

${\textbf{Step -1: Label the points as given}}{\mathbf{(1,2),(1,3),(1,-4),(1,0),(1,8)}}{\textbf{.}}$

${\textbf{Step -2: Draw a line passing through all the points}}{\textbf{.}}$

${\text{When a line is drawn passing through all the points we see that it passes}}$

${\text{ parallel to the }}y - {\text{axis}}.$

${\textbf{Hence, The points given form a straight line which passes parallely from }}\mathbf{y -} {\textbf{axis}}{\text{.}}$

Draw the graph of $\sin x$ .

1187747_1299726_ans_f25205ba9d2844e4bea03c1220df197f.jpg

(5,4),(8,4),(3,4),(0,4),(-4,4),(-2,4) ? locate the points points on graph sheet .

We have,

Given points are

$\left( {{x}_{1}},{{y}_{1}} \right)=\left( 5,4 \right)$

$\left( {{x}_{2}},{{y}_{2}} \right)=\left( 8,4 \right)$

$\left( {{x}_{3}},{{y}_{3}} \right)=\left( 0,4 \right)$

$\left( {{x}_{4}},{{y}_{4}} \right)=\left( -4,4 \right)$

$\left( {{x}_{5}},{{y}_{5}} \right)=\left( -2,4 \right)$

Then,

Locate above picture
1219864_1312112_ans_46fbdf5411854fe5923cceaf4b57a98c.png

The number of room in $25$ houses of a locality is as given below:
$4,3,2,6,4,3,2,1,5,3,2,3,4,3,5,1,6,1,3,4,2,3,4,3,5$
Draw bar graph to represent the above date.

We can draw the bar graph by following the given steps:

Step

$1:$ On a graph paperdraw a horizontal line

$OX$ as

$x-$ axis and vertical line

$OY$ as

$y-$ axis.

Step

$2:$ Along

$OX,$ write the years at the points that are taken at a uniform gap.

Step

$3:$ Choose the scale

$1$ month

$=2$ rooms

Step

$4:$ Draw bars of equal width on the

$x-$ axis.The difference between the two bars should be the same.

We get the following bar graph:

1480528_1353819_ans_c48788fa077542e1af1dc8a32dbf853d.png

The adjoining bar graph shows the numbers of book sold by a bookstore during $5$ consecutive years. Read the bar graph and answer the following question:
About how many books were sold in $2008, 2009$ and $2011$ years?

Books sold in

$2008=120$

Books sold in

$2009=320$

Books sold in

$2011=200$

Books were sold in

$2008,\,2009$ and

$2011$ years

$=120+320+200=640$

The following bar graph shows the percentage of chairs produced by two companies Neel Kamal and Raj Kamal during five different years. Bar graph also shows the total no. of chairs produced in different years associated with it. Study the graph carefully to answer the following questions:
$i)$ Find the average no. of chairs produced by Raj Kamal in the years 2004, 2006 and 2007 together.
$ii)$ What is the ratio of no. of chairs produced by Neel Kamal in the years 2007 and 2008 together to that by Raj Kamal in the same years together?
$iii)$ If 12% chairs out of total chairs produced in the year 2008 were defective and in them ratio of defective chairs by Raj Kamal and Neel Kamal is 2 : 3 then find the no. of defective chairs produced by Neel Kamal in the year 2008.

$i)\dfrac{1}{3}\times \left(54 \times 150 + 60 \times 300 + 36 \times 450\right)$

$=\dfrac{1}{3}\times 42300$

$= 14100$ .

$ii)$ Required ratio of chairs $= \dfrac{64 \times 450 + 56 \times 500}{36 \times 450 + 44 \times 500}$

$= \dfrac{56800}{38200}$

$= \dfrac{284}{191}$ .

$iii)$ Required number of chairs $=\dfrac{3}{5}\times \dfrac{12}{100} \times 50000= 3600$ .

The number of pressure cookers produced in a factory for five consecutive months is given below:
Month
January
February
March
April
May
Number of pressure cookers produced
780
1100
920
1040
1280
Draw a bar graph representing the above information.

We can draw the bar graph by following the given steps:

Step

$1:$ On a graph paperdraw a horizontal line

$OX$ as

$x-$ axis and vertical line

$OY$ as

$y-$ axis.

Step

$2:$ Along

$OX,$ write the years at the points that are taken at a uniform gap.

Step

$3:$ Choose the scale

$1$ month

$=100$ pressure cookers produced

Step

$4:$ Draw bars of equal width on the

$x-$ axis.The difference between the two bars should be the same.

We get the following bar graph:

1480536_1465767_ans_bf351c49b7a043deb5a7f7dc43eed629.png

The table below shows the number of people who had the different juices at a juice bar on a Saturday and Sunday. Draw a joint bar graph for this data.
fruits
day Sweet lime Orange Apple Pineapple
Saturday $43$ $30$ $56$ $40$
Sunday $59$ $65$ $78$ $67$

$\Rightarrow$ The above figure shows required joint bar graph.

$x-axis$ contains different fruit juices.

$y-axis$ contains number of people who had juices.

1234819_1402035_ans_1311cefde6c64ac883d4b00bcaa176d5.jpeg

Why do we group data?

Grouped data are data formed by aggregating individual observations of a variable into groups, So that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data these are two major types of grouping data binning of a single dimensional variable, replacing individual numbers by counts in, and grouping multidimensional (especially by independent variables) obtaining the distribution of ungrouped dimensions (especially the dependent variables).

Find the coordinates of points $A, B, C, D$

$A(1,1),B(1,4),C(4,6),D(5,3)A(1,1),B(1,4),C(4,6),D(5,3)$

Read the bar graph given in fig. and answer the following questions:
What was the crop- production of rice in 1970-71? (in lakh tonnes)

The crop production of rice in

$1970 - 71 = 42. 5$ lakh tonnes.

Draw the temperature -time graph in each of the following cases:
Time(in hours): $7:00$ $9:00$ $11:00$ $13:00$ $15:00$ $17:00$ $19:00$ $21:00$
Temperature ( $^{0}F$ )in: $100$ $101$ $104$ $102$ $100$ $99$ $100$ $98$

1483186_1674120_ans_4e0ebfe7a9c84505814df52e782348df.jpg

The following data give the amount of loans (in crores of rupees) disbursed by a bank during some years :
Year 1992 1993 1994 1995 1996
Loan
(in crores of rupees ) 28 33 55 55 80
Represent the above data with the help of a bar graph.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the amount of loan in Crores of rupees respectively.

We have to draw

$5$ bars of different lengths given in the table. At first, we mark

$5$ points in the horizontal axis at equal distances and erect rectangles of the same width at these points.

The heights of the rectangles are proportional to the amount of loan disbursed by the bank.

The vertical bar graph of the given data is following:

1482635_1671098_ans_1d7182a15a0a42a08687ecc48b2a9770.png

The following table shows the interest paid by a company (in lakhs) :
Year 1995-96 1996-97 1997-98 1998-99 1999-2000
Interest
(in lakhs of rupees ) 20 25 15 18 30
Draw the bar graph to represent the above information.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the interests in lakhs of rupees respectively. We have to draw

$5$ bars of different lengths given in the table.

At first, we mark

$5$ points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the interests paid by the company.

The vertical bar graph of the given data is following:

1482634_1671140_ans_9d3ccaae2a27480ea10adfc98ab46a3b.png

The income and expenditure for 5 years of a family is given in the following data :
Years 1995-96 1996-97 1997-98 1998-99 1999-2000
Income
(RS in thousands ) 100 140 150 170 210
Expenditure
(RS in thousands ) 80 130 145 160 190
Represent the above data by a bar graph.

1872105_1671255_ans_7c75bfea76f04635834c9ede02ac6752.png

Draw the velocity-time graph from the following data:
Time(in hours): $7:00$ $8:00$ $9:00$ $10:00$ $11:00$ $12:00$ $13:00$ $14:00$
Speed(in km/hr): $30$ $45$ $60$ $50$ $70$ $50$ $40$ $45$

1483188_1674131_ans_1e0ae00e60fc41999c459464f4fed914.jpg

The expenditure (in 10 crores of rupees) on health by the Government of India during the various five year plans is shown below :
Plans : $I$ $II$ $III$ $IV$ $V$ $VI$
Expenditure on health
(in 10 crores of rupees ) 7 14 23 34 76 182
Construct a bar graph to represent the above data.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes.

Let us consider that the horizontal and vertical axes represent the years and the expenditures on health in

$10$ Crores rupees respectively. We have to draw

$6$ bars of different lengths given in the table.

At first, we mark

$6$ points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the expenditures on health by the government of India in different years.

The vertical bar graph of the given data is following:

1482625_1671327_ans_534d371f310047148db05560da95d2e9.png

Read the graph given in above fig. and answer the following question:
What is the information given by the bar graph?

1671133_1671174_ans_60b561be88494d88ba6105cc0ea2ee6b.jpg

Read the bar graph shown in fig. and answer the following question:
What is the information given by the bar graph?

Tickets of different state lotteries sold by an agent on a day is the information given by the bar graph.

Read the bar graph shown in Fig. and answer the following questions:
What is the information given by the bar graph?

Number of commercial banks over the years is the information given by the bar graph.

The above table shows the percentage of students who dropped out of school after completing high school.
Study the above table carefully and draw a line graph to depict it.

Consider, year on the

$x- axis$ and the percentage of students who dropped out of school on the

$y-axis$ .

The line graph is represented in the figure.

1617916_1775152_ans_d1c6e9b5cb394a2c95d1da87b8719e92.png

Consider the above input/output table. Draw a line graph for it.
Now, use the graph drawn to predict the outputs for the inputs of $3$ and $8$

Consider the input on the

$X – axis$ and output on the

$Y- axis$ . The line graph is represented in figure.

From the graph the outputs for the inputs

$3$ and

$8$ is

$8$ and

$23.$

1617819_1775148_ans_369adcc3d14a4c99b6b0eaa7c70c252c.png

The above table depicts the maximum temperature on the seven days of a particular week. Study the table and draw a line graph for the same.

Taking the days on the X – axis and maximum temperature on the Y- axis, the line graph is obtained as in the figure above.

1617796_1775146_ans_cdbd249eaace406fa51114362c340aac.png

The table given above depicts the annual gross profit of a company for a period of 5 years. Study the table and draw a line graph for the same.

Consider the year on the X – axis and gross profit on the Y- axis. The line graph is represented in figure.

1617835_1775150_ans_e0fd384562bc41f9a7520607bcac575d.png

The above chart gives the growth in height in terms of percentage of full height of boys and girls with their respective ages.
Study the table and draw the line graph of the data given above:
Now, use the graph to answer the following questions:
i. In which year both the boys and the girls achieve their maximum height?
ii. Who grows faster at puberty (14 years to 16 years of age)?

The line graph is represented in the figure:

i. In the

$18^{th}$ year both boys and girls achieve their maximum height.

ii. Boy's {from 92% to 98%} grow faster than girls {from 98% to 99.5%} at puberty.

1618243_1775156_ans_32177799a44146138ef1075ebe743cc8.png

For an experiment in botany, two different plants, plant A and plant B, were grown under similar laboratory conditions. Their heights were measured at the end of each week for three weeks. The results are shown by the line graph given above:
Study the above graph carefully and answer the questions given below:
i. How high was plant A after (a) 2 weeks (b) 3 weeks?
ii. How high was plant B after (a) 2 weeks (b) 3 weeks?
iii. How much did plant A grow during the $3^{rd}$ week?
iv. How much did plant B grow from the end of the $2^{nd}$ week to the end of the $3^{rd}$ week?
v. During which week did plant A grow most?
vi. During which week did plant B grow least?
vii. Were the two plants of the same height during any week shown here? Specify

i. Plant A was

$(a) \, 7 \,cm$ high after

$2 \,weeks \,(b) \, 9 \,cm$ high after

$3 \,weeks.$

ii. Plant B was (a)

$7 \,cm$ high after

$2 \,weeks \,(b) \,10 \,cm$ high after

$3 \,weeks.$

iii. During the

$3^{rd}$ week plant A grew

$9-7=2 \,cm.$

iv. From the end of

$2^{nd}$ week to the end of

$3^{rd}$ week plant B grew

$10-7=3 \,cm.$

v. Plant A grew most in the

$2^{nd}$ week.

vi. Plant B grew least in the

$1^{st}$ week.

vii. Yes, as seen in the graph the two plants were of same height at the end of

$2^{nd}$ week.

A car is travelling from city P to city Q, which are $350 \,km$ apart. The line graph given below describes the distance of the car from the city P at different times.
Study the above graph and answer the questions given below

i.What information is given on the two axes?
ii.From where and when did the car begin its journey?
iii.How far did the car go in the first hour?
iv.How far did the car go during (a) the $2^{nd}$ hour (b) the $3^{rd}$ hour?
v.Was the speed same during first three hours? How do you know it?
vi.Did the car stop for some duration at any place? Justify your answer.
vii.When did the car reach the city Q?

i. On the two axes – the

$X$ -axis shows the time and

$Y$ -axis shows the distance of the car from city

$P.$

ii. The car begins its journey from city P at

$8:00$ a.m.

iii. The car covered a distance of

$50\,km$ in the

$1^{st}$ hour.

iv. The car covered a distance of:

(a)

$150-100=100\, km$ in the

$2^{nd}$ hour.

(b)

$200-150=50\,km$ in the

$3^{rd}$ hour.

v. No the speed was not same, because the distance covered per hour is not uniform.

vi. Yes, the car stopped at a place during the time interval

$11$ a.m. to

$12$ a.m. as indicated by horizontal line segment during this period.

vii. At

$2$ p.m. the car reached at the city

$Q$ .

The following is the distance-time graph of Amits walking.
Study the above graph carefully and answer the questions given below:
i. When does Amit make the least progress? Explain your answer.
ii. Find his average speed in km/hr.

i. As indicated by the line in the graph, Amit makes the least progress from

$25 \,min$ to

$40 \,min.$

ii. We know that the total distance covered by Amit is

$2 \,km$ and the time taken is

$55 \,min$ i.e.

$55/60 \,hour.$

By using the formula,

Average speed =

$\dfrac{total \ distance \ covered} {time \ taken}$

$= \dfrac 2 {(55/60)}\,km/hour = \dfrac 2{55} \times 60\,km/hour = 2.18 \,km/hour$

The line graph given above shows the yearly sales figures for a manufacturing company during the last five years.
Study the above graph carefully and answer the questions given below:
i. What were the sales in $(a) \,2013 \,(b) \,2015 \,(c) \,2016$
ii. Compute the difference between the sales in $2012$ and $2016$ ?
iii. In which year was there the greatest difference between the sales as compared to its previous year?

i. The sales in

$(a) \,2013$ is

$Rs.7\,cr \,(b) \,2015$ is

$Rs.10 \,cr \,(c) \,2016$ is

$8 \,cr$

ii. The difference between the sales in

$2012$ and

$2016$ is

$=8-4=Rs. 4 \,cr$

iii. Difference at every year

$2013-2012=|7-4|=3$

$2014-2013=|8-6|=2$

$2015-2014=|10-6|=4$

$2016-2015=|10-8|=2$

The greatest difference of sales was seen in the year

$2015.$

A courier person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distances from the town at different times are shown by the given graph.
Study the above graph carefully and answer the questions given below:
i. What is the scale taken for the time axis?
ii. How much time did the person take for the travel?
iii. How far is the place of the merchant from the town?
iv. Did the person stop on his way? Explain.
v. During which period did he ride fastest?

i. The scale taken for the time axis is

$4\ \text{unit} =1 \ \text{hour} \text{ or } 1 \,\text{unit}=15 \,\text{minutes.}$

ii. Total time of travel of the person

$=14\times15=210\ \text{minutes}=3 \,\text{hours 30 minutes}$

iii. Clearly, The distance from the town to the merchant place is

$22 \,\text{km}.$

iv. Yes, the person stopped on his way during the time interval

$10 \,\text{a.m.}$ to

$10:30\, \text{a.m.}$ as indicated by the horizontal line on the graph.

v. During

$8 \,\text{a.m.}$ to

$9 \,\text{a.m.}$ period he rode the fastest.

A man started his journey on his car from location A and came back. The graph given below shows his position at different times during the whole journey.
Study the above graph carefully and answer the questions given below:
i. At what time did he start and end his journey?
ii. What was the total duration of the journey?
iii. Which journey, onwards or return, was of longer duration?
iv. For how many hours did he not move?
v. At what time did he have the fastest speed?

i. The start journey was at

$5.30$ a.m and the end journey was at

$6$ p.m.

ii. The total duration of the journey was

$12 \,hour \,30 \,minutes.$

iii. onward journey took

$8:30\ hours$ and return journey took

$4\ hours$

$\therefore$ The onward journey took longer duration.

iv. He did not move for

$6 \,hours.$ (from

$6$ am to

$9$ am and

$10$ am to

$1$ pm)

v. During

$2 \,p.m$ to

$6 \,p.m$ period he had the fastest speed.(As the distance traveled with respect to time is maximum.)

The horizontal and vertical lines in a line graph are usually called _ and __ .

The horizontal and vertical lines in a line graph are usually called x-axis and y-axis .

The total number of people surveyed is_______

The correct fill up is

$35$ .

Total number of people surveyed=

$8+14+5+6+2=35.$

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which subject did she score the highest in test l?

Observing the graph, we conclude that

In Maths, she scored the highest in Test I.

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
What information is represented by the axes?

Observing the graph, we conclude that

The x-axis represents subjects and the y-axis represents marks of Sonia.

The graph given below gives the actual and expected sales of cares of a company for $6$ months. Study the graph and answer the questions that follow.
In which month was the actual sales same as the expected sales?

In April, the actual sales was same as the expected sales.

Side (in $cm^2$ ) 1 2 3 4
Area (in $cm^2$ ) 1 4 9 16
Make a line graph for the area of a square as per the given table.
Is it linear graph?

According to the given data, the following graph is plotted.

It can be observed that the graph is not linear.

1689906_1794308_ans_d53eb498e1f94a3a9762b332c8f3e84b.png

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.
What information is given by the two axes?

In the given graph,

The x-axis shows 'days of a particular week' and y-axis shows 'the maximum temperature recorded'.

The graph given below gives the actual and expected sales of cars of a company for $6$ months. Study the graph and answer the questions that follow.
Find the ratio of sales in the first three months to the last three months.

The number of sales of car in the first three months

$= 250$ and

The number of sales of car in the last three months

$= 375$

The required ratio is

$250 : 375=\dfrac{250}{375}=\dfrac23=2:3$

The graph given below gives the actual and expected sales of cares of a company for $6$ months. Study the graph and answer the questions that follow.
For which month (s) was (were) the difference in actual and expected sales the least?

In April, the difference in actual and expected sales was the least.

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.
In which week was the temperature higher on most of the days?

$\text{first week}$ the temperature was higher on most of the days

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.
On which day was the temperature same in both the weeks?

$\text{wednesday}$ the temperature was same in both the weeks

The graph given below gives the actual and expected sales of cares of a company for $6$ months. Study the graph and answer the questions that follow.
For which month (s) was (were) the difference in actual and expected sales the maximum?

In March, the difference in actual and expected sales was the maximum.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
Calculate the average speed of the man from
(a) A to B
(b) B to C

Observing the graph, we conclude that,

Average speed from A to B

$= \dfrac{\text{Distance travelled}}{\text{Time taken}}=4$ km/h and

Average speed from B to C

$= \dfrac{\text{Distance travelled}}{\text{Time taken}}=0$ km/hr.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
What was he doing from $3$ pm to $5$ ?

Observing the graph, we conclude that,

He was taking rest from 3 PM to 5 PM.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
What was the total distance travelled by him throughout the day?

Observing the graph, we conclude that,

The distance covered by the person throughout the day was 20 km from A to S and then 20 km from C to D

So, Total travelled distance

$=20 + 20 = 40$ km.

Study the graph given below of a person who started from his home and returned at the end of the day. Answer the following question.
How much distance did he travel in the first four hours of his journey?

Observing the graph, we can conclude that,

In first four hours (i.e. from

$10\ am$ to

$2\ pm$ ), he travelled

$16\ km$ .

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
Calculate the distance croved by him in the first $8$ hours of his journey.

Observing the graph, we conclude that,

The distance covered by him in the first 8 h i.e. from 10 AM to 6 PM was 24 km.

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which subject did she score the least in test ll ?

Observing the graph, we conclude that

In English and Hindi, she scored the least in Test II.

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which test was the performance better?

Observing the graph, we conclude that

In both tests, her performance is same.

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which subject and which test did she score full marks?

Observing the graph, we conclude that

Test I in Maths, she scored full marks i.e. 10 marks.

Plot a line graph for the variables $p$ and $q$ where $p$ is two times $q$ i.e, the equation is $p =2q$ . Then find the value of p when $q = 3$

1918571_1794479_ans_d5d874b739c2400daaaadb96795ff5e3.jpg

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which subject did she score the same marks in both the Tests?

Observing the graph, we conclude that

In Hindi and Maths, she scored the same marks in both tests.

The following table gives the growth chart of a child.
Draw a line graph for the table and answer the questions that follow.
What is the height at the age of 5 years?

Plot the points

$(75,2), (90,4), (110,6),(120,8)$ and

$(130,10)$ .

Using the data given in the chart, the graph between the height and age of a child is shown above.

From the graph, we see that height is

$100\text{ cm}$ at the age of

$5$ years.

1884430_1794539_ans_a8433e6a2ac84b4698443a0db4e544ea.png

The following is the time-distance graph of Sneha's walking
When does Sneha make the least progress ? Explain your reasoning.

From the graph we can say that , Sneha made the least progress from the interval 25 minutes to 40 minutes.

We see that initially , she is travelling approximately 0.5 km in 10 min , 0.25 km in 5 min , till the first 25 mins. But after 25 mins, her speed decreased as she travelled 0.25 km in 15 min.

We can say that because of her speed in that interval i.e. (0.25 km) / (15 min) = (0.25km) / (0.25 hr) = 1 km/hr which the lowest among all.

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
On which two days was the sales same for vendor B?

From the graph, we can see that, the sales are same on Tuesday and Wednesday for vendor B ( 30 ice cream ).

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
What is the change in temperature between $7$ am and $10$ am?

From the graph,

Temperature at 7 am = 5°C

Temperature at 10 am = 8°C

Hence, the change of 3°C is observed between 7 am and 10 am.

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
On which day did the sale of vendor A increase the most as compared to the previous day?

From the graph, we can see that, the sales for Vendor A increase the most on Saturday as compared to the previous day.

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
During which hour did the temperature fall?

From the graph, it can be observed that the temperature falls between 5 AM - 6 AM.

Plot a line graph for the variables $p$ and $q$ where $p$ is two times $q$ i.e, the equation is $p=2q$ . Then find the value of $q$ when $p=8$ .

Given equation is

$p=2q$

Thus,

for

$q=1\ ,\ \ p=2$

for

$q=2\ ,\ \ p=4$

for

$q=3\ ,\ \ p=6$

for

$q=4\ ,\ \ p=8$

Now we tabulate the data and the graph is plotted as shown.

Hence, when

$p=8$ then the value of

$q=4$

1690237_1794481_ans_eb4b03edf95b47a88c855343ab9e3175.png

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
For which day was the sales same for both the vendors?

From the graph, we can see that, the sales is same for both the vendors on Sunday.

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:
For how long was there a change in temperature?

From the graph, the temperature of the ice changes for 30 seconds i.e. from 20 to 50 seconds.

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:
For how many second did the ice block have no change in temperature?

From the graph, it is clear that the temperature of ice does not changes for first 20 seconds ( from 0 to 20 seconds at 0°C )

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.
What was the total duration of journey?

From the graph, the man started his journey at 5:30 AM and ended at 6 PM.

Hence the total duration of journey is 12 hours and 30 minutes.

The following graph shows the number of people present at a certain at different times. Observe the graph and answer the following questions.
What is the busiest time of day at the shop?

From the graph, we can say that the busiest time of day at the shop is 1:00 PM i.e. maximum 25 people are present at that time.

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.
At what time did he start and end his journey?

From the graph, we can say that , the man started his journey at 5:30 AM and ended at 6 PM.

The following graph shows the number of people present at a certain at different times. Observe the graph and answer the following questions.
What type of a graph is this?

In the given graph only line are there and so, the graph is a line graph.

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.
Which journey, forward of return, was of longer duration?

From the graph, it is clear that the forward journey is of 8 hours and 30 minutes ( 5:30 AM to 2:00 PM ) and the backward journey is of 4 hours ( 2:00 PM to 6:00 PM ).

Hence, Forward journey is of longer duration.

The following graph shows the number of people present at a certain at different times. Observe the graph and answer the following questions.
What information does the graph give?

The given graph gives us the information about number of people present in a certain shop at a particular time.

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:
What was the temperature after $25$ seconds?

From the graph, we can say that after 25 seconds the temperature of the ice is 20°C.

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:
What will be the temperature after $1.5$ minutes?

From the graph, we can say that after 50 seconds the temperature become constant at 100°C for infinite time. Hence, we can conclude that the temperature is 100°C after 1.5 minutes.

The following graph shows the change in temperature of a block of ice when heated. Use the graph to answer the following questions:
After how many seconds of heating did the temperature become constant at $100^{o}$ C?

From the graph, we can see that the after heating for 50 seconds the temperature of ice become constant at 100°C.

The following graph shows the number of people present at a certain at different times. Observe the graph and answer the following questions.
How many people are there in the shop at $1.30$ pm?

From the graph, 20 people are there in the shop at 1:30 PM.

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.
For how many hours did he not move?

From the graph, man is at rest when the line is horizontal.

Hence, the man did not move for 6 hours ( 6:30 AM to 9:30 AM and 10:00 AM to 1:00 PM).

The following graph shows the journey made by two cyclists, one from A to B and The other from town B to A.
at what time did the two cyclists meet?

They will meet when their journey lines intersect.

From the graph, it is clear that they will meet at 9:00 AM.

The table shows the data collected for Dhruv's walking pn a road
Plot a line graph for the given data using suitable sacle.
In what time periods did Dhruv make the most progress?

A) Using the given values in the chart, the graph between Distance travelled (

$Y$ -axis ) and time taken (

$X$ -axis ) by Dhruv is shown above.

B) By observing the data, we get

Time interval

$= 0 - 5$ , Distance

$= 0.5$

Time interval

$= 5 - 10$ , Distance

$= 0.5$

Time interval

$= 10 - 15$ , Distance

$= 0.25$

Time interval

$= 15 - 20$ , Distance

$= 0.25$

Time interval

$= 20 - 25$ , Distance

$= 0.25$

Hence, the most progress is done by Dhruv in time interval (

$0$ to

$5$ min ) and (

$5$ to

$10$ min ).

1884125_1794591_ans_d1ffa4ceef7a482480737043a3fd63f7.png

A man started his journey on his car from location A and came back. The given graph shows his position at different times during the whole journey.
At what time did he have the fastest speed?

It is clear from the graph the man travelled fastest speed between 1:00 PM to 2:00 PM i.e. he travelled 60 KM in just one hour.

The following chart gives the growth in hight in terms of percentage of full height of boys and girls with their respective ages.
Draw the line graph of above data on the same sheet and answer the following questions.
In which year both the boys and the girls achieve their maximum height?

A) Using the data given in the chart, the graph between the growth in heights of boys and girls ( Y-axis ) with their respective ages ( X- axis ) is shown above.

B) It is clear from the graph that the girls achieve 100 % in 17 years of age and boys in 18 years of age.

So, boys in the age of 18 and girls in the age of 17 years achieve their maximum height.

1884142_1794588_ans_377e50feae0743b9a9172f973b70f99b.png

The following graph shows the journey made by two cyclists, one from A to B and The other from town B to A.
How far had cyclist ll travelled when he met cyclist l ?

The cyclist || travels from Town B to A i.e. he starts his journey at 10:00 AM and met cyclist || at 9:00 AM.

Hence for cyclist ||, at 10:00 AM - Distance from town A is 30 KM

and at 9:00 AM - Distance from town A is 10 KM.

Hence, Cyclist || had travelled 20 KM when he met cyclist |.

Ajita starts off home at $7.00$ hours with her father oon a scooter that goes at a uniform speed of $30$ km/h and drops her school after half an hour she stays in the school till $13.30$ hours and takes an auto rickshaw to return home the rickshaw has a uniform speed of 10 km/h. Draw the graph for the above situation and also determine the distance of Ajita's school from her house.

1884170_1794586_ans_a59b37ed273149b991434ba769910bb1.jpeg

Draw the line graph suitable scale to how the annual gross profit of a company for a period of five years.

The line graph that shows the annual gross profit of a company for a period of five years are shown above.

In the graph Gross Profit ( in Lakhs ) is represented on Y-axis and Year is represented on X-axis.

1884149_1794587_ans_100acc1ae06c4ef18b6b720fc34d3157.png

The following graph shows the journey made by two cyclists, one from A to B and The other from town B to A.
At what time did cyclist ll rest? How long the cyclist rest?

Dotted line represents the journey of cyclist ll , and in the graph distance travelled is represented on Y-axis and Time is on X-axis.

Hence, the cyclist || will rest when he travelled zero distance i.e. between 8:45 to 9:00 AM , distance travelled is zero.

So, the cyclist || rests between 8:45 to 9:00 AM and for 15 minutes.

The following chart gives the growth in hight in terms of percentage of full height of boys and girls with their respective ages.
Draw the line graph of above data on the same sheet and answer the following questions.
Who grows faster at puberty $(14$ years to $16$ years of age)?

A) Using the data given in the chart, the graph between the growth in heights of boys and girls ( Y-axis ) with their respective ages ( X- axis ) is shown above.

B) As shown in the graph the line of girls is higher than the line of boys means that the girls grow faster at puberty ( 14 to 16 years of age ).

1884137_1794589_ans_28e284f7126549f5961cc0f9d70289cd.png

Input 1 2 4 5 7
Output 2 5 11 14 20
Consider this input/output table.
Use your graph to predict the outputs for inputs of 3 and 8.

In the previous question, by plotting the graph of input and output we figured out that the graph follows the line y = 3x - 1.

So, for x = 3 , then y = ( 3 x 3 ) - 1 = 8

and for x = 8, then y = ( 3 x 8) - 1 = 23

Input	3	8
Output	8	23

1882944_1795242_ans_3c78ecc4b5404fd2a0324c45973b36c2.png

This graph shows the percent of students who dropped out of school after completing High School. The point labeled A shows that, in 1996, about $4.7%$ of students dropped
About what percent of students dropped out of high school in 2007? About what percent of students stayed in high school in 2008?

It is given that , in 1996 about 4.7 % students dropped out.

By observing the graph , the percentage of dropped out students is slightly higher in 2007 than in 1996.

So, approximately we can say that in 2007, 4.8% students dropped out.

Now, in 2008 the percentage of dropped out students decreased that means some students stayed and we can say approximately 0.1% percent student stayed in high school

Observe the given graph carefully and complete the table given below.

By observing the given graph, we can say that

When,

x = 1 → y = 2.5

x = 2 → y = 5

x = 3 → y = 10

x= 4 → y = 15

x = 5 → y = 20

Now, rewriting it in tabular form, we get

x	1	2	3	4	5
y	2.5	5	10	15	20

This graph shows the percent of students who dropped out of school after completing High School. The point labeled A shows that, in 1996, about $4.7%$ of students dropped
In which year was the dropout the rate highest? In which year was it the lowest?

The graph shown in the question shows the percent of students who dropped out of school after completing High School year-wise.

The maxima and minima of the graph will show the highest and lowest dropout rate.

Maxima - 1990

Minima - 2000

So, the dropout rate is highest in year 1990 and lowest in year 2000.

This graph shows the percent of students who dropped out of school after completing High School. The point labeled A shows that, in 1996, about $4.7%$ of students dropped
When did the percent of students who dropped out of high school first fall below $5%$ ?

After observing the given graph , it is clear that the percent of students who dropped out of high school first fall below 5 is in year 1996.

Find the quartile deviation and coefficient of quartile deviation of the following data.
$3 , 8, 11, 13, 17, 19, 20 , 22, 23, 27, 31$

Given data is in assending order .
Total number of terms

$N = 11$

$Q _{1} =$ value of

$\dfrac{11+1}{4}$ the term
= Value of

$\dfrac{12}{4}$ th term
= Value of 3rd term

$=11$

$Q_{3}$
= Value of

$\dfrac{3 (N + 1)}{4}$ th term
= Value of

$\dfrac{3(11 + 1)}{4}$ th term
= value of

$3 \times \dfrac{12}{4}$ th term
= Value of 9th term

$= 23$
Quartile deviation (Q.D)

$= \dfrac{Q_{3} - Q_{1}}{2} = \dfrac{12}{2} = 6$ Coeficient of quartile =

$\dfrac{Q_{3} - Q_{1}}{Q_{3} + Q_{1}}$

$= \dfrac{23 - 11}{23 + 11} = \dfrac{12}{14} = 0.352$
Thus quartile deviation 6 and its coeficient 0.352

For any variable series $Q_{1} 61$ and $Q_{3} = 121$ . Find the quartile deviation

Quartile deviation ( Q. D) =

$\dfrac{Q_{3} - Q_{1}}{2}$

$\dfrac{121-61}{2}$

$\dfrac{60}{2} = 30$

Write the formula of quartile deviation

Coefficient of quartile deviation

$\dfrac{Q_{3} - Q_{1}}{Q_{3} + Q_{1}}$
Hence ,

$Q_{3}$ = upper quartile ,

$Q_{1}$ = Lower quartile .

Explain any two requisites of a good table. Also draw a specimen table and label it properly.

The essentials of good tables includes: headings, abbreviations, footnote and total in table. In singular form heading should be written.
In heading abbreviation should not be used in heading, footnote should be used if necessary and in the ending of per row sub-total should be used.

Following is a specimen table with proper labeling.

2136281_2019791_ans_101d0e5f45824cb1b2a7ccd10b33b392.PNG

X 6 2 10 4 8
Y 9 11 5 8 7
Find the coefficient of correlation.

Answer is as follows:
2144277_2024439_ans_e322a6b201844b62bae56d835ccca79d.jpeg

The heights of a group of fathers and son are given below:
Height of father (in inches) 65 66 67 67 68 68 70 73
Height of son (in inches) 67 68 64 69 72 71 69 72
Calculate Karl pearson coefficient of correlation.

2142566_2023111_ans_b2d85a46182d42f6b0eff7ded26b995f.jpeg

Calculate Karl Pearson coefficient of skewness when mean=20, mode=18, and SD=3.

2143230_2023439_ans_fceb50d7b41a49f18338174eb3872fb7.png

Define dispersion.

The word dispersion stands for ‘distribution’ of things over a wide area. In statistics, the extent to which the numerical data are distributed or squeezed about an average value is called dispersion. In short, it is the distribution of data.

Read the following passage and answer the given questions, Karl Pearson (1867-1936) was the first person to give mathematical formula for measuring the degree of relationship between two variables inThe Karl Pearson's coefficient of correlation is also known as 'Product Moment Correlation' or 'Simple Correlation Coefficient". It is the most popular and widely used method to calculate the correlation coefficient. It is denotes by (r is a pure number, i.e it has no unit).
i) Name the first person to give mathematical formula for measuring the degree of relationship between two variables in 1980.
ii) The Karl Pearson's coefficient of correlation is also known as _ or ____.

(i) Karl Pearson is the first person to give mathematical formula for measuring the degree of relationship between two variables in 1980.

ii) The Karl Pearson's coefficient of correlation is also known as Product Moment Correlation or Simple Correlation Coefficient..

A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.

Dispersion is the extent to which values in a distribution differ from the avarage of the distribution. Knowledge of only average is insufficient as it does not reflect the quantum of variation in values. Measures of dispersion enhance the understanding of a distribution considerably by providing information about how much the actual value of items in a series deviate from the central value, e.g., per capita income gives only the average income but a measure of dispersion can tell you about income inequalities, thereby improving the understanding of the relative living standards of different sections of the society. Through value of dispersion one can better understand the distribution. Thus a measure of dispersion is a good supplement to the central value in understanding a frequency distribution.

Find the quartilc deviation of $6, 12, 14, 16,18, 20$ and $24$

Step

$1 :$ Arranging the numbers in ascending order

$6,12,14,16,18,20,24$

Step

$2 :$ Dividing the data in two sets below and above the median by placing parenthesis

$(6,12,14), 16 ,(18,20,24)$

Step

$3 :$ Find

$Q_{1}$ and

$Q_{3}$ ,

$Q_{1}$ is median of lower half of data and

$Q_{3}$ is median of upper half of data

$Q_{1} = 12$

$Q_{3} = 20$

Step

$4 :$ Quartile Deviation

$= \dfrac{Q_{3}-Q_{1}}{2}$

$Q_{2} = \dfrac{20-12}{2} = 4$

The following table shows the amount of rice grown by a farmer in different years:
Years Rice grown (in qt.)
2000 200
2001 180
2002 240
2003 260
2004 250
2005 200
2006 270
Plot a bar graph to illustrate the above information. The number of years having the highest production then the preceding years are

Year	2000	2001	2002	2003	2004	2005	2006
Rice grown(in qty)	200	180	240	260	250	200	270

The number of years having the highest production then the preceding years are 4(2000, 2002, 2003, 2006)

1022616_302811_ans_8aca7bf24453459f87c73675d1a29486.jpg

1022616_302811_ans_8aca7bf24453459f87c73675d1a29486.jpg

What are the different types of table?

Statistical tables can be classified under two general categories, namely, general tables and summary tables.

What do you mean by "Tabulation of data"?

Tabulating is a way of processing information or data by putting it in a table. This doesn't mean the kind of table you eat off of, though. It refers to a table, or chart, with rows and columns. When tabulating, you might have to make calculations.

Tabulation is a mechanical function of classification because is tabulation classified data are placed in row and columns. ... Classification is a process of statistical analysis while tabulation is a process of presenting data is suitable struture.

In a bar graph, the height of a bar is proportional to the ________

In a bar graph,the height of a bar is proportional to the value of variable shown on y-axis.

Draw a bar chart of the data representing pass $\%$ of students during the period $1998-2003$ given below :
Year 1998 1999 2000 2001 2002 2003
Pass % 80% 75% 90% 70% 95% 85%

1203467_1248983_ans_4b48caff87b5459aaede71a13b70c78a.jpg

Which is the highest peak and what is it's height?

$Heighest\, \, peak\, \, is\, \, Mount\, \, Everest\, \, with\, \, a\, \, height\, \, of\, about\, \, 8800\, \, metre.$

Draw bar graphs to show the following:
Days Attendance in Class
Mon. 30
Tues. 28
Wed. 25
Thurs. 29
Fri. 34
Sat. 32

Given that

Days Mon Tues Wed Thus Fri Sat

Attendance in class

$30$

$28$

$25$

$29$

$34$

$32$

Bar graph: It is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.

1475264_1369315_ans_58fceb5c06d241efaa2d8864ce169626.png

Write the height of the given peaks in ascending order.

$\begin{matrix} Annapurna<Himadri<Nanda\, \, devi<Nangaparbat \\ <Kangchenjung<Mount\, \, Everest \\ \end{matrix}$

Which peak is second highest and what is its height ?

$\begin{matrix} { Sec }ond\, \, heighest\, \, peak\, \, is\, \, kangchenjung\, \, a \\ peak\, \, with\, \, a\, \, heighest\, \, of\, about\, \, 8500\, \, metres. \\ \end{matrix}$

The final marks in mathematics of 30 students are as follows:
$53,61,48,60,78,68,55,100,67,90$
$75,88,77,37,84,58,60,48,62,56$
$44,58,52,64,98,59,70,39,50,60$
What is the highest score?

Given that final marks in mathematics of 30 students are as follows:

$53,61,48,60,78,68,55,100,67,90$

$75,88,77,37,84,58,60,48,62,56$

$44,58,52,64,98,59,70,39,50,60$

first of all arrange the marks as groups ascending order means lowest number to highest number

Group	Ascending order
30 to 39	37, 39
40 to 49	44, 48, 48
50 to 59	50, 52, 53, 55, 56, 58, 58, 59
60 to 69	60, 60, 60, 61, 62, 64, 67, 68
70 to 79	70, 75, 77, 78
80 to 89	84, 88
90 to 100	90, 98, 100

We observe that

Highest score

$= 100$

The production of saleable steel in some of the steel plants of our country during 1999 is given below:
Plant Bhilai Durgapur Rourkela Bokaro
Production (In thousand tonnes) 160 80 200 150
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousand tonnes.

Given that

the production of sales able steel in some of the steel plants of our country during

$1999$ is

Plant Bhilai Durgapur Rourkela Bokaro

Production(in thousand formers)

$160$

$80$

$200$

$150$

Scale

$1$ big division

$=20$ thousand formers)

1480970_1675500_ans_5ec9904215b148dcb594414c6a322b80.png

The weights of new born babies (in kg) in a hospital on a particular day are as follows:
$2.3,2.2,2.1,2.7,2.6,3.0,2.5,2.9,2.8,3.1,2.5,2.8,2.7,2.9,2.4$
How many babies weigh below 2.5 kg?

given weights if now born (in kg) in a hospital on a particular day are as follows

$2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4$

first all arrange the data in as ascending order

$2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1$

Number of new born babies weigh below

$2.5kg$ is 4

In a mathematics test following marks were obtained by 40 students of class VI. Arrange these marks in a table using, tally marks.
8 1 3 7 6 5 5 4 4 2
4 9 5 3 7 1 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6
How many students obtained marks below 4?

In a mathematics test following marks were obtained by

$40$ students of class VI.

Arrange these marks in table, tally marks

Marks Frequency Tally marks

$1$

$2$ ||

$2$

$3$ |||

$3$

$3$ |||

$4$

$7$ ||||

$5$

$6$ ||||

$6$

$7$ ||||

$7$

$5$ ||||

$8$

$4$ ||||

$9$

$3$ |||

Total

$40$

No. of students obtained marks equal to more than

$7$ (

$7, 8, 9$ marks) is

$=5+4+3$ $

$=12$

No. of students obtained marks below

$4$ is i.e.,

$(3, 2, 1$ marks)

$=3+3+2$

$=8$ .

The following data gives the number (in thousands) of applicants registered with an Employment Exchange during. 1995-2000:
year 1995 1996 1997 1998 1999 2000
Number of applicants registered (in thousands) 18 20 24 28 30 34
Construct a bar graph to represent the above data.

Given that

the number(in thousands) of applicants registered with an employment echange during

$1995-2000$

Year

$1995$

$1996$

$1997$

$1998$

$1999$

$2000$

No. of applicants registered(in thousands)

$18$

$20$

$24$

$28$

$30$

$34$

On x-axis

$1$ cm

$=1$ year

on y-axis

$1$ cm

$=10$ units.

1480973_1675512_ans_0e54c8de7fe04d6995fa99ad73fc9fce.png

Calculate the Karl Pearson's coefficient of correlation between years of schooling of farmers and the annual yield per acre in (Rs.000).
No. of years of schooling of farmers Annual yield per acre (in Rs.'000)
0 4
2 4
4 6
6 10
8 10
10 8
12 7

Solution is as follows:

2146908_2026091_ans_b289fc945ad945f0aff476bffc2300e3.PNG

The following graph shows the journey made by two cyclists, one from A to B and The other from town B to A.
When cyclist ll reached town A, how far was cyclist l from town B?

1976545_1794584_ans_eeb919b3d47f43a0bad382264651ff96.jpeg

Calculate the Sk (Skewness) and comment on the result.

X

X²

10

100

12

144

18

324

24

576

64

4,096

Comment: Since the value of skewness is more than 1, so data are highly skewed.
2158985_2032872_ans_25fb60fac35749a29f39e6ce76cdab1f.PNG

Thee two graph below compare Car A and Care B. The left graph shows the relationship between age and value. The right graph shows the relationship between size and maximum speed.
Use the graphs to determine whether each statement is ture or false, and explain your answer.
The more valuable car is slower.

1976559_1795267_ans_ec09d09fc5394b4b96d4b67e3a6409c8.jpeg

Name of the animals	Goat	Horse	Cow	Camel	Elephant
Age (in years)	$12$	$15$	$15$	$26$	$60$

Months	Jan	Feb	Mar	Apr	May	Jun	Jul
Number of sandwiches sold	12	23	15	10	25	16	22

Class	Fifth	Sixth	Seventh	Eighth	Ninth	Tenth
Number of children	$135$	$120$	$95$	$100$	$90$	$80$

Year	1941	1951	1961	1971	1981	1991	2001
Population	320	360	440	550	680	850	1000

Year	$1941$	$1951$	$1961$	$1971$	$1981$	$1991$	$2001$
Population (in millions)(approx.)	$320$	$360$	$440$	$550$	$680$	$850$	$1000$

Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
$35.5$	$30.8$	$27.3$	$32.1$	$23.8$	$29.9$

Students	Ajay	Bali	Dipti	Faiyaz	Geetika	Hari
Marks obtained	$450$	$500$	$300$	$360$	$400$	$540$

Deposit (in Rs.)	1000	2000	3000	4000	5000
Simple Interest (in Rs.)	80	160	240	320	400

Class interval	frequency
$1 - 9$	$4$
$10 - 19$	$3$
$20 - 29$	$20$
$30 - 39$	$12$
$40 - 49$	$5$
$50 - 59$	$8$
$60 - 69$	$14$
$70 - 79$	$27$
$80 - 89$	$2$
$90 - 99$	$5$

Class interval	frequency
$5 - 15$	$11$
$15 - 25$	$5$
$25 - 35$	$15$
$35 - 45$	$9$
$45 - 55$	$22$
$55 - 65$	$8$
$67 - 75$	$17$

Marks scored	$10$	$20$	$30$	$40$	$50$	$60$
No. of students	$12$	$7$	$16$	$8$	$18$	$22$

$C.I.$	$0-9$	$10-19$	$20-29$	$30-39$	$40-49$	$50-59$	$60-69$
$f$	$8$	$16$	$17$	$34$	$10$	$5$	$10$

Month	Sale (in Rs)
March	2000
April	2500
May	4500
June	3000
July	4000
August	3500

fruits day	Sweet lime	Orange	Apple	Pineapple
Saturday	$43$	$30$	$56$	$40$
Sunday	$59$	$65$	$78$	$67$

Time(in hours):	$7:00$	$9:00$	$11:00$	$13:00$	$15:00$	$17:00$	$19:00$	$21:00$
Temperature ( $^{0}F$ )in:	$100$	$101$	$104$	$102$	$100$	$99$	$100$	$98$

Year	1992	1993	1994	1995	1996
Loan (in crores of rupees )	28	33	55	55	80

Year	1995-96	1996-97	1997-98	1998-99	1999-2000
Interest (in lakhs of rupees )	20	25	15	18	30

Years	1995-96	1996-97	1997-98	1998-99	1999-2000
Income (RS in thousands )	100	140	150	170	210
Expenditure (RS in thousands )	80	130	145	160	190

Time(in hours):	$7:00$	$8:00$	$9:00$	$10:00$	$11:00$	$12:00$	$13:00$	$14:00$
Speed(in km/hr):	$30$	$45$	$60$	$50$	$70$	$50$	$40$	$45$

Plans :	$I$	$II$	$III$	$IV$	$V$	$VI$
Expenditure on health (in 10 crores of rupees )	7	14	23	34	76	182

Descriptive Statistics - Class 11 Commerce Applied Mathematics - Extra Questions

The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it. EnglishHindiMathsScienceSocial Studies8585 6060 3535 5050 7070

Draw a bar-graph (chart) to represent the following data:Name of the animalsGoatHorseCowCamelElephantAge (in years)12121515151526266060

Find the quartile deviation of 6, 12,14, 16, 18, 20 and 24.

MonthsJan Feb Mar Apr May Jun Jul Number of sandwiches sold 12 23 15 10 25 16 22 Draw the line graph for the following data.

Write the coordinates of the vertices of each of these adjoining figures.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:Political Party AB C D E F Seats Won 75 55 37 29 1037 (i) Draw a bar graph to represent the polling results.(ii) Which political party won the maximum number of seats?

Identify the scale used on the axes of the adjacent graph. Write the frequency distribution from it

Find the median and quartile deviation for the following data.xx3344556677ff12123535525241411818

The marks scored by 66 students in a preparatory exam are given here:56,71,49,90,8856, 71, 49, 90,88.Find the median score and semi-quartile range

The coefficient of variations of two series are 5858 and 6969. Their standard deviations are 21.221.2 and 15.615.6. What are their arithmetic means?

If the point (3, 4)(3, 4) lies on the graph of the equation 3y=ax+73y=ax+7, fine the values.

Number of children in six different classes are given. Represent the data on a bar graph.ClassFifthSixthSeventhEighthNinthTenthNumber of children135135120120959510010090908080Answer the following question.Find the ratio of students of class sixth to the students of class eight.

Draw a bar graph for the following data.Population of India in successive census years:Year1941195119611971198119912001Population3203604405506808501000

Match the values of \varrho _{1},\varrho _{2},\varrho _{3}\varrho _{1},\varrho _{2},\varrho _{3} for the following data values13,14,7,12,17,8,10,6,15,18,21,2013,14,7,12,17,8,10,6,15,18,21,20

When the scale along the x-axis does not start at the origin, we show it by a kink (break or a zig - zag curve of the origin). What is a kink? Why it is used?

Draw a bar graph for the following data.Population of India in successive census years.Year19411941195119511961196119711971198119811991199120012001Population (in millions)(approx.)32032036036044044055055068068085085010001000Source: Data from census of India 19911991 and 20012001.

In a survey of 300300 families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given:Read the graph carefully and answer the following questions:What percentage of the families have 44 children ?

The daily temperature recorded (in degree FF) at a place during a week was as under:MondayTuesday Wednesday ThursdayFriday Saturday35.535.530.830.827.327.332.132.123.823.829.929.9Calculate the mean temperature.

In what ways is the bar graph better than pictography.

A number of children in six different classes are given below. Represent the data on the bar graph:

In a survey of 300300 families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given:Read the graph carefully and answer the following questions:How many family have no child?

Whose savings in the month of April is the least?

In a survey of 300300 families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given: Read the graph carefully and answer the following question: How many family have 22 children each?

Were the two plants of the same height during any week shown here? specify.

The number of books issued from a library in five days is given below. Represent the information in the form of a bar graph.

_______ displays data that changes continuously over periods of time.

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.At what time did the person start from his home?

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.On which day was the difference in temperatures the maximum for both the weeks?

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.At what time did he cover 1616 km of his journey ?

The graph given below gives the actual and expected sales of cars of a company for 66 months. Study the graph and answer the questions that follow.What are the average sales of cars in the last three months?

The graph given below gives the actual and expected sales of cars of a company for 66 months. Study the graph and answer the questions that follow.What was the total sale of cars in the months- Jan, Feb, and March?

The following table gives the growth chart of a child.Draw a line graph for the table and answer the questions that follow.How much taller was the child at the age of 10 than at the age of 66 ?

The table given below shows the temperatures recorded on a day at different times.Observe the table and answer the following questions.At what time is the temperature 3^{o}3^{o} C?

The following is the time-distance graph of Sneha's walkingFind her average speed in km/hour.

The graph given below compares the sales of ice creams of two vendors for a week.Observe the graph and answer the following questions.Which vendor has sold more ice cream on Friday?

The points on the graph below represent the height and weight of the donkey, dog, crocodile, and ostrich shown in the drawing.What are the two variables represented in the graph?

The graph given below compares the sales of ice creams of two vendors for a week.Observe the graph and answer the following questions.On which day was the difference in sales the maximum?

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.At what time did he return home ?

The table given below shows the temperatures recorded on a day at different times.Observe the table and answer the following questions.What is the temperature a t88 am?

The number of days a hillside city received snow in different years.Year20032003200420042005200520062006Days881010551212

To get an interest of Rs. 280 per year,how much money should be deposited?answer required

Given the marks scored by Rita's out of 100, in five subjects in a particular test.SubjectMarksEnglish78Hindi72Maths96Science88S.St80Can we draw the bar graph for above data?If yes enter 1 else 0.

Following data gives total marks (out 600600) obtained by six children of a particular class. Represent the data on a bar graph.StudentsAjayBaliDiptiFaiyazGeetikaHariMarks obtained450450500500300300360360400400540540

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.(i) Represent the information above by a bar graph.(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Draw a graph for the following.i) Side of square (in cm) 23 3.5 5 6 Perimeter (in cm) 812 14 20 24 Is it a linear graph?(ii) Side of square (in cm) 23 45 6 Perimeter (in cm) 49 16 25 36 Is it a linear graph?

The given graph represent the how much consumers would be willing to pay for store brand and brand name products. On average, how many more cents are consumers willing to pay for the brand name version of the product than the store brand version? (Round your answer to the nearest cent)

Calculate quartile deviation for the following data:30, 18, 23, 15, 11, 29, 37, 42, 10, 2130, 18, 23, 15, 11, 29, 37, 42, 10, 21

Calculate quartile deviation for the following data:3, 5, 8, 10, 12, 7, 53, 5, 8, 10, 12, 7, 5

Compute quartile deviation for each of the following tables.Class intervalfrequency1 - 91 - 94410 - 1910 - 193320 - 2920 - 29202030 - 3930 - 39121240 - 4940 - 495550 - 5950 - 598860 - 6960 - 69141470 - 7970 - 79272780 - 8980 - 892290 - 9990 - 9955

Calculate quartile deviation for the following data:Age33669912121515No. of children44881111771212

Compute quartile deviation for each of the following tables.Class intervalfrequency5 - 155 - 15111115 - 2515 - 255525 - 3525 - 35151535 - 4535 - 459945 - 5545 - 55222255 - 6555 - 658867 - 7567 - 751717

Calculate quartile deviation for the following data:Marks scored101020203030404050506060No. of students12127716168818182222

Calculate the quartile deviation for the following:C.I.C.I.0-90-910-1910-1920-2920-2930-3930-3940-4940-4950-5950-5960-6960-69ff881616171734341010551010

The runs scored by a batsman in seven innings are 28, 60, 85, 58, 74, 20, 9028, 60, 85, 58, 74, 20, 90. Find Q_{1}, Q_{2}, Q_{3}Q_{1}, Q_{2}, Q_{3} and quartile deviation

Define or explain the concepts:Higher Order Table

Define or explain the concepts:Complex table

Give Reason :Manifold table can presents 2 or 3 characteristics.

What are the different types of tables?

Define or explain the concepts:Complex Table

Answer the Following :What is a complex table?

Define or explain the concepts:Tabulation

Write Short Note on the following:Types of Table

Draw a graph for the data given in the table. Hence find the number of days taken by 1212 workers to complete the work ?No. of works xx3468916No. of days yy967248363218

Sita practiced piano for 2hrs everyday during the month of January. How many hrs did she practice in January? (Use bar model for solving the sum)

Number of children in six different classes are given. Represent the data on a bar graph.ClassFifthSixthSeventhEighthNinthTenthNumber of Children135135120120959510010090908080How would you choose a scale?

Number of children in six different classes are given. Represent the data on a bar graph.ClassFifthSixthSeventhEighthNinthTenthNumber of Children135135120120959510010090908080Answer the following question.Which class has the maximum number of children? And the minimum?

Draw a pic chart for the following data.Item of expenditureFoodHealthClotingEducation SavingsAmount spent in rupess3750375018751875187518751200120075007500

Draw a bar graph ..The number of saplings planted by a former in five consecutive weeks are given below.

How much more is the total saving of Savita than the total saving of Megha?

How much is the saving of Vaishali in the month of April?

MonthSale (in Rs) March2000 April2500 May 4500 June3000 July4000 August 3500 Daily sales (in Rs) of Sushil Enterprises from March to August are given below :Draw a bar graph to depict the above data.

How much is the total saving of Saroj in the months March and April?

The names and number of animals in a certain zoo are given below. use the data to make a bar graph. (Scale : on Y-axis, 1 cm =4 animals)AnimalsDeer Tiger Monkey Rabbit Peacock Number 20 4 12 16 8

What is the percentage increase of earning from Thursday to friday ?

What can you say about the position of the points (1,2,),(1,3),(1,-4),(1,0) and (1,8) locate on graph sheet

Draw the graph of \sin x\sin x.

(5,4),(8,4),(3,4),(0,4),(-4,4),(-2,4) ? locate the points points on graph sheet .

The number of room in 2525 houses of a locality is as given below:4,3,2,6,4,3,2,1,5,3,2,3,4,3,5,1,6,1,3,4,2,3,4,3,54,3,2,6,4,3,2,1,5,3,2,3,4,3,5,1,6,1,3,4,2,3,4,3,5Draw bar graph to represent the above date.

The adjoining bar graph shows the numbers of book sold by a bookstore during 55 consecutive years. Read the bar graph and answer the following question: About how many books were sold in 2008, 20092008, 2009 and 20112011 years?

The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it.
English
Hindi Maths
Science
Social Studies
$85$
$60$
$35$
$50$
$70$

Draw a bar-graph (chart) to represent the following data:
Name of the animals
Goat
Horse
Cow
Camel
Elephant
Age (in years)
$12$
$15$
$15$
$26$
$60$

Months Jan Feb Mar Apr May Jun Jul
Number of
sandwiches sold 12 23 15 10 25 16 22
Draw the line graph for the following data.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
Political Party A B C D E F
Seats Won 75 55 37 29 10 37
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?

Find the median and quartile deviation for the following data.
$x$ $3$ $4$ $5$ $6$ $7$
$f$ $12$ $35$ $52$ $41$ $18$

The marks scored by $6$ students in a preparatory exam are given here:
$56, 71, 49, 90,88$ .
Find the median score and semi-quartile range

The coefficient of variations of two series are $58$ and $69$ . Their standard deviations are $21.2$ and $15.6$ . What are their arithmetic means?

If the point $(3, 4)$ lies on the graph of the equation $3y=ax+7$ , fine the values.

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of children $135$ $120$ $95$ $100$ $90$ $80$
Answer the following question.
Find the ratio of students of class sixth to the students of class eight.

Draw a bar graph for the following data.
Population of India in successive census years:
Year 1941 1951 1961 1971 1981 1991 2001
Population 320 360 440 550 680 850 1000

Match the values of $\varrho _{1},\varrho _{2},\varrho _{3}$ for the following data values
$13,14,7,12,17,8,10,6,15,18,21,20$

Draw a bar graph for the following data.
Population of India in successive census years.
Year $1941$ $1951$ $1961$ $1971$ $1981$ $1991$ $2001$
Population (in millions)(approx.) $320$ $360$ $440$ $550$ $680$ $850$ $1000$
Source: Data from census of India $1991$ and $2001$ .

What percentage of the families have $4$ children ?

The daily temperature recorded (in degree $F$ ) at a place during a week was as under:
Monday Tuesday Wednesday Thursday Friday Saturday
$35.5$ $30.8$ $27.3$ $32.1$ $23.8$ $29.9$

Calculate the mean temperature.

In a survey of $300$ families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given:Read the graph carefully and answer the following questions:
How many family have no child?

In a survey of $300$ families of a colony, the number of children in each family was recorded and the data has been represented by the bar graph, given: Read the graph carefully and answer the following question: How many family have $2$ children each?

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did the person start from his home?

The graph shows the maximum temperatures recorded for two consecutive weeks of a town. Study the graph and answer the questions that follow.
On which day was the difference in temperatures the maximum for both the weeks?

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did he cover $16$ km of his journey ?

The graph given below gives the actual and expected sales of cars of a company for $6$ months. Study the graph and answer the questions that follow.
What are the average sales of cars in the last three months?

The graph given below gives the actual and expected sales of cars of a company for $6$ months. Study the graph and answer the questions that follow.
What was the total sale of cars in the months- Jan, Feb, and March?

The following table gives the growth chart of a child.
Draw a line graph for the table and answer the questions that follow.
How much taller was the child at the age of 10 than at the age of $6$ ?

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
At what time is the temperature $3^{o}$ C?

The following is the time-distance graph of Sneha's walking
Find her average speed in km/hour.

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
Which vendor has sold more ice cream on Friday?

The points on the graph below represent the height and weight of the donkey, dog, crocodile, and ostrich shown in the drawing.
What are the two variables represented in the graph?

The graph given below compares the sales of ice creams of two vendors for a week.
Observe the graph and answer the following questions.
On which day was the difference in sales the maximum?

Study the graph given below of a person who stared from his home and returned at the end of the day. Answer the questions that follow.
At what time did he return home ?

The table given below shows the temperatures recorded on a day at different times.
Observe the table and answer the following questions.
What is the temperature a t $8$ am?

The number of days a hillside city received snow in different years.
Year $2003$ $2004$ $2005$ $2006$
Days $8$ $10$ $5$ $12$

To get an interest of Rs. 280 per year,how much money should be deposited?

answer required

Given the marks scored by Rita's out of 100, in five subjects in a particular test.
Subject Marks
English 78
Hindi 72
Maths 96
Science 88
S.St 80
Can we draw the bar graph for above data?
If yes enter 1 else 0.

Following data gives total marks (out $600$ ) obtained by six children of a particular class. Represent the data on a bar graph.
Students Ajay Bali Dipti Faiyaz Geetika Hari
Marks
obtained $450$ $500$ $300$ $360$ $400$ $540$

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Draw a graph for the following.

i)
Side of square (in cm) 2 3 3.5 5 6
Perimeter (in cm) 8 12 14 20 24
Is it a linear graph?

(ii)
Side of square (in cm) 2 3 4 5 6
Perimeter (in cm) 4 9 16 25 36
Is it a linear graph?

Calculate quartile deviation for the following data:
$30, 18, 23, 15, 11, 29, 37, 42, 10, 21$

Calculate quartile deviation for the following data:
$3, 5, 8, 10, 12, 7, 5$

Compute quartile deviation for each of the following tables.
Class interval frequency
$1 - 9$ $4$
$10 - 19$ $3$
$20 - 29$ $20$
$30 - 39$ $12$
$40 - 49$ $5$
$50 - 59$ $8$
$60 - 69$ $14$
$70 - 79$ $27$
$80 - 89$ $2$
$90 - 99$ $5$

Calculate quartile deviation for the following data:
Age $3$ $6$ $9$ $12$ $15$
No. of children $4$ $8$ $11$ $7$ $12$

Compute quartile deviation for each of the following tables.
Class interval frequency
$5 - 15$ $11$
$15 - 25$ $5$
$25 - 35$ $15$
$35 - 45$ $9$
$45 - 55$ $22$
$55 - 65$ $8$
$67 - 75$ $17$

Calculate quartile deviation for the following data:
Marks scored $10$ $20$ $30$ $40$ $50$ $60$
No. of students $12$ $7$ $16$ $8$ $18$ $22$

Calculate the quartile deviation for the following:
$C.I.$ $0-9$ $10-19$ $20-29$ $30-39$ $40-49$ $50-59$ $60-69$
$f$ $8$ $16$ $17$ $34$ $10$ $5$ $10$

The runs scored by a batsman in seven innings are $28, 60, 85, 58, 74, 20, 90$ . Find $Q_{1}, Q_{2}, Q_{3}$ and quartile deviation

Define or explain the concepts:
Higher Order Table

Define or explain the concepts:
Complex table

Give Reason :

Manifold table can presents 2 or 3 characteristics.

Define or explain the concepts:
Complex Table

Answer the Following :
What is a complex table?

Define or explain the concepts:
Tabulation

Write Short Note on the following:

Types of Table

Draw a graph for the data given in the table. Hence find the number of days taken by $12$ workers to complete the work ?
No. of works
$x$
3 4 6 8 9 16
No. of days
$y$ 96 72 48 36 32 18

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of Children $135$ $120$ $95$ $100$ $90$ $80$
How would you choose a scale?

Number of children in six different classes are given. Represent the data on a bar graph.
Class Fifth Sixth Seventh Eighth Ninth Tenth
Number of Children $135$ $120$ $95$ $100$ $90$ $80$
Answer the following question.
Which class has the maximum number of children? And the minimum?

Draw a pic chart for the following data.
Item of expenditure Food Health Cloting Education Savings
Amount spent in rupess $3750$ $1875$ $1875$ $1200$ $7500$

Draw a bar graph ..
The number of saplings planted by a former in five consecutive weeks are given below.

Month Sale (in Rs)
March 2000
April 2500
May 4500
June 3000
July 4000
August 3500
Daily sales (in Rs) of Sushil Enterprises from March to August are given below :
Draw a bar graph to depict the above data.

The names and number of animals in a certain zoo are given below. use the data to make a bar graph. (Scale : on Y-axis, 1 cm =4 animals)
Animals Deer Tiger Monkey Rabbit Peacock
Number 20 4 12 16 8

Draw the graph of $\sin x$ .

The number of room in $25$ houses of a locality is as given below:
$4,3,2,6,4,3,2,1,5,3,2,3,4,3,5,1,6,1,3,4,2,3,4,3,5$
Draw bar graph to represent the above date.

The adjoining bar graph shows the numbers of book sold by a bookstore during $5$ consecutive years. Read the bar graph and answer the following question:
About how many books were sold in $2008, 2009$ and $2011$ years?

The number of pressure cookers produced in a factory for five consecutive months is given below:
Month
January
February
March
April
May
Number of pressure cookers produced
780
1100
920
1040
1280
Draw a bar graph representing the above information.

The table below shows the number of people who had the different juices at a juice bar on a Saturday and Sunday. Draw a joint bar graph for this data.
fruits
day Sweet lime Orange Apple Pineapple
Saturday $43$ $30$ $56$ $40$
Sunday $59$ $65$ $78$ $67$

Find the coordinates of points $A, B, C, D$

Read the bar graph given in fig. and answer the following questions:
What was the crop- production of rice in 1970-71? (in lakh tonnes)

Draw the temperature -time graph in each of the following cases:
Time(in hours): $7:00$ $9:00$ $11:00$ $13:00$ $15:00$ $17:00$ $19:00$ $21:00$
Temperature ( $^{0}F$ )in: $100$ $101$ $104$ $102$ $100$ $99$ $100$ $98$

The following data give the amount of loans (in crores of rupees) disbursed by a bank during some years :
Year 1992 1993 1994 1995 1996
Loan
(in crores of rupees ) 28 33 55 55 80
Represent the above data with the help of a bar graph.

The following table shows the interest paid by a company (in lakhs) :
Year 1995-96 1996-97 1997-98 1998-99 1999-2000
Interest
(in lakhs of rupees ) 20 25 15 18 30
Draw the bar graph to represent the above information.

The income and expenditure for 5 years of a family is given in the following data :
Years 1995-96 1996-97 1997-98 1998-99 1999-2000
Income
(RS in thousands ) 100 140 150 170 210
Expenditure
(RS in thousands ) 80 130 145 160 190
Represent the above data by a bar graph.

Draw the velocity-time graph from the following data:
Time(in hours): $7:00$ $8:00$ $9:00$ $10:00$ $11:00$ $12:00$ $13:00$ $14:00$
Speed(in km/hr): $30$ $45$ $60$ $50$ $70$ $50$ $40$ $45$

The expenditure (in 10 crores of rupees) on health by the Government of India during the various five year plans is shown below :
Plans : $I$ $II$ $III$ $IV$ $V$ $VI$
Expenditure on health
(in 10 crores of rupees ) 7 14 23 34 76 182
Construct a bar graph to represent the above data.

Read the graph given in above fig. and answer the following question:
What is the information given by the bar graph?

Read the bar graph shown in fig. and answer the following question:
What is the information given by the bar graph?

Read the bar graph shown in Fig. and answer the following questions:
What is the information given by the bar graph?

The above table shows the percentage of students who dropped out of school after completing high school.
Study the above table carefully and draw a line graph to depict it.

Consider the above input/output table. Draw a line graph for it.
Now, use the graph drawn to predict the outputs for the inputs of $3$ and $8$

The following is the distance-time graph of Amits walking.
Study the above graph carefully and answer the questions given below:
i. When does Amit make the least progress? Explain your answer.
ii. Find his average speed in km/hr.

The horizontal and vertical lines in a line graph are usually called _ and __ .

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
In which subject did she score the highest in test l?

The graph given below shows the marks obtained out of $10$ by Sonia in two different tests. Study the graph and answer the questions that follow.
What information is represented by the axes?

The graph given below gives the actual and expected sales of cares of a company for $6$ months. Study the graph and answer the questions that follow.
In which month was the actual sales same as the expected sales?

Height of father (in inches)	65	66	67	67	68	68	70	73
Height of son (in inches)	67	68	64	69	72	71	69	72

Years	Rice grown (in qt.)
2000	200
2001	180
2002	240
2003	260
2004	250
2005	200
2006	270

Days	Attendance in Class
Mon.	30
Tues.	28
Wed.	25
Thurs.	29
Fri.	34
Sat.	32

Plant	Bhilai	Durgapur	Rourkela	Bokaro
Production (In thousand tonnes)	160	80	200	150

No. of years of schooling of farmers	Annual yield per acre (in Rs.'000)
0	4
2	4
4	6
6	10
8	10
10	8
12	7