MCQ Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 2

A symbol is used to represent

$10$ flowers. Number of symbols to be drawn to show

$60$ flowers is ___

0%
$6$
0%
$12$
0%
$11$
0%
$10$

Explanation

A symbol is used to represent

$10$ flowers

Number of symbols to be drawn to represent

$60$ flowers

$=\dfrac{60}{10}=6$

$1000$ TV sets were sold in the year

0%
$1985$
0%
$1990$
0%
$1980$
0%
$2000$

Explanation

Answer:- Converting the whole pictograph into frequency distribution table-

Year	No. of TV sets sold $\left( in symbol \right)$ $\left( f_i \right)$	Actual no. of T sets sold $\left( f_i \times 500 \right)$
$1980$	$2$	$1000$
$1985$	$5$	$2500$
$1990$	$3$	$1500$
$1995$	$1$	$500$
$2000$	$5$	$2500$

$1000$ TV sets sold in year

$1980$ .

$C) 1980$

On joining the points if we get a straight line, that graph is called.

0%
Bar graph
0%
Pie chart
0%
Line graph
0%
None of these

The line graph shows the monthly expenditure of Vasu family. The total expenditure over the first

$3$ months is

0%
$Rs. 320$
0%
$Rs. 600$
0%
$Rs. 1100$
0%
$Rs. 1400$

Explanation

In the graph, 1 unit on y-axis

$=Rs.100$

The monthly expenses of Basu family in the month of

In January, the expenditure is marked upto

$5$ units

$=Rs.500$

In February, the expenditure is marked upto

$6$ units

$=Rs.600$

In March, the expenditure is marked upto

$3$ units

$=Rs.300$

$\therefore$ The total expenditure over the first

$3$ months

$=Rs.(500+600+300)$

$=Rs.1400$

Answer the following question by reading the given pictograph.

Number of TV sets sold in the year 2000 is

0%
1990
0%
1995
0%
2008
0%
2000

Explanation

From the given pictograph,

$2000$ has three tv symbol.

Given that one symbol represents

$500$ tv sets.

Therefore the

$2000$ has

$3\times500= 1500$ tv sets.

The variance of first n natural numbers is

0%
$\displaystyle \frac{n^2 + 1}{12}$
0%
$\displaystyle \frac{n^2 - 1}{12}$
0%
$\displaystyle \frac{n^2 - 1}{6}$
0%
$\displaystyle \frac{n^2 + 1}{2}$

Explanation

$\textbf{Step - 1: Finding the mean}$

$\text{The } n \text{ natural numbers are } 1, 2, 3,..., n$

$\text{The Sum of } n \text{ natural number is } \dfrac{{n(n+1)}}{{2}}$

$\text{Mean} = \dfrac{ \dfrac{{n(n+1)}}{{2}}}{n} = \dfrac{{n+1}}{{2}}$

$\textbf{Step - 2: Finding the Variance}$

$\text{Variance} = \dfrac{{\sum(x_i)^2}}{{n}} - (\text{Mean})^2$

$\sum(x_i)^2 = \dfrac{{1^2 +2^2 + ...+ n^2}}{{n}}$

$\text{Since } 1^2 +2^2 + ...+ n^2 = \dfrac{{n(n+1)(2n+1)}}{{6}}$

$\dfrac{{\sum(x_i)^2}}{{n}} = \dfrac{{n(n+1)(2n+1)}}{{6n}}$

$\text{Variance} = \dfrac{{n(n+1)(2n+1)}}{{6n}} - (\dfrac{{n+1}}{{2}})^2$

$=\dfrac{{(n+1)}}{{2}}\times(\dfrac{{2n+1}}{{3}}-\dfrac{{n+1}}{{2}})$

$= \dfrac{{(n+1)}}{{2}}(\dfrac{{4n+2-3n-3}}{{6}})$

$=\dfrac{{n+1}}{{2}}\times\dfrac{{n-1}}{{6}}$

$= \dfrac{{n^2 - 1}}{{12}}$

${\textbf{Hence, the correct answer is Option B}.}$

The formula of standard deviation of a grouped frequency distribution is

0%
$\displaystyle\sqrt{\frac{\sum{(x_i-\bar{x})^2}}{N}}$
0%
$\displaystyle\frac{\sum{(x_i-\bar{x})^2fi}}{N}$
0%
$\displaystyle\sqrt{\frac{\sum{(x_i-\bar{x})^2fi}}{N}}$
0%
$\displaystyle\frac{\sum{(x_i-\bar{x})^2fi}}{fi}$

Explanation

Formula to calculate Standard deviation of a grouped frequency distribution is

$\sqrt { \frac { \sum { { (x }_{ i }-\bar { x } )^{ 2 } } { f }_{ i } }{ N } }$
where

$f_1$ is the frequency of observation

$x_i$ ;

$bar {x}$ is the mean of the frequency distribution

$N$ is the sum of all frequencies

On which day the bus was most crowded?

0%
Friday
0%
Saturday
0%
Sunday
0%
Monday

Explanation

$\Rightarrow$ From the pictograph we are going to form the following table :

$Days$	$No.\,of\,persons$
$Monday$	$9$
$Tuesday$	$4$
$Wednesday$	$6$
$Thursday$	$4$
$Friday$	$8$
$Saturday$	$7$
$Sunday$	$2$

$\Rightarrow$ From the table we can see, bus was most crowded on

$Monday.$

If the standard deviation for the marks obtained by a student in monthly tests is 36 then the variance is

0%
6
0%
36
0%
1296
0%
none of these

Explanation

Standard deviation defined the square root of varian

Standard deviation=

$\sqrt{variance}$

Given Standard deviation=36

$36=\sqrt{V}$ (where V is s tendered deviation

Square both sides

$(36)^{2}=V\Rightarrow V=1296$

Which one of the following statements is correct?

0%
The standard deviation for a given distribution is the square ofthe variance
0%
The standard deviation for a given distribution is the square root of the variance
0%
The standard deviation for a given distribution is equal to the variance
0%
The standard deviation for a given distribution is halfofthe variance

Explanation

We know that

$Variance=\dfrac{\sum{fD^2}}{N}$

$Standard\ Deviation (SD)=\sqrt{Variance}$

Hence, The Standard deviation for a given distribution is the square root of the variance.

Hence, this is the answer.

Five chemical factories

$P,\,Q,\,R,\,S\;and\;T$ are located in different cities along a river bank. Municipal officer, in order to estimate the pollution caused by these factories, counted the number of fishes present at the places where these factories discharged their wastes into the river. A graph as shown here, is plotted based on the observations.
What can be inferred from the graph ?

0%
Factory $R$ dumps the least toxic wastes in the river.
0%
Factory $P$ dumps its waste into river after removing toxic wastes.
0%
Fishes are maximally harmed by the toxic wastes of factory $Q$ .
0%
Factory $T$ dumps the most toxic wastes in the river.

Explanation

Because the number of fishes present in the river where factory

$T$ dump the waste is less than any other so factory

$T$ dumps the most toxic wastes in the river.
Hence option

$D$ is answer.

Which is the highest peak?

0%
A
0%
E
0%
C
0%
B

Explanation

$\Rightarrow$ We form a table from given graph.

$Mountains$	$Height$ $(meters)$
$A$	$8200$
$B$	$6000$
$C$	$8600$
$D$	$7500$
$E$	$8800$
$F$	$6500$

$\Rightarrow$ From above table we can see that mountain

$E$ has highest height

$8800\,meters$ .

$\therefore$

$E$ is the highest peak.

The difference in the sales of apple products for the year

$2000$ and

$2001$ is?

0%
$4000$
0%
$3000$
0%
$2000$
0%
$1000$

Explanation

The difference in the sales of apple products for the year

$2000$ and

$2001$ is

$4000 - 3000 = 1000$ .

The sum of sales of apple products in the years

$1999$ and

$2000$ is approximately equal to that in?

0%
$1998$
0%
$2001$
0%
$2002$
0%
$2003$

Explanation

The sum of sales in two years is:

$1200 + 3000 = 4200$
Which approximately equal to

$4000$ in the year

$2001$ .

The percentage increases in sales from

$2000$ to

$2003$ was?

0%
$55.44\%$
0%
$56.89\%$
0%
$66.66\%$
0%
$89.56\%$

Explanation

The percentage increase

$=$

$\dfrac{5000 - 3000}{3000}\times 100$

$\%$

$= 66.66\%$

What is the ratio between total sales rate of apple product in the year

$2001$ to

$2003$ ?

0%
$5:4$
0%
$4:3$
0%
$4:5$
0%
$5:3$

Explanation

Ratio of sales rate of apple product in the year

$2001$ to

$2003$ is

$4000:5000$
So, it is

$4:5$

Johnson's pickle factory exports bottles of pickle. The pictograph shows the number of bottles exported each day. Use the information from the graph to answer the questions.

(

$1$ pickle jar

$= 500$ )

On which day they export less number of pickle bottles?

0%
Monday
0%
Tuesday
0%
Wednesday
0%
Thursday

Explanation

From the pictograph, they export

$8$ bottles on Monday,

$5$ on Tuesday,

$3$ on Wednesday,

$8$ on Thursday and

$6$ on Friday

So, they export less number of pickle bottles on Wednesday.

The picture graph below shows the number of shirts ordered in each size in one week
Which size of shirts were ordered exactly 15 shirts?

0%
Small
0%
Medium
0%
Large
0%
Extra Large

Explanation

From the given pictograph, small size have 5 symbol.

Given that one symbol represents 3 shirts.

Therefore

$\displaystyle 5 \times 3 = 15$ shirts were ordered of small size.

When the heights of the given peaks are written in ascending order then what is the average of the middle two peaks?

0%
7950 m
0%
7560 m
0%
7650 m
0%
7850 m

Explanation

The ascending order of heights is

$6000 m<6500 m<7500m<$

$8200m<8600m<8200m.$
The two middle peaks are

$7500$ m and

$8200$ m
Average =

$\displaystyle \dfrac{7500+8200}{2}$

$\displaystyle \frac{15700}{2}=7850m$

Which of the following represents data that continuously changes over periods of time?

0%
Bar graph
0%
Circle graph
0%
Histogram
0%
Line graph

Which of the two days did they export more bottles of pickles?

0%
Monday and Wednesday
0%
Thursday and Friday
0%
Monday and Thursday
0%
Tuesday and Friday

Explanation

From the pictograph, they export

$8$ bottles on Monday,

$5$ on Tuesday,

$3$ on Wednesday,

$8$ on Thursday and

$6$ on Friday.

So, Monday and Thursday are the two days when they export more bottles of pickles.

_______ is the graphical representation of statistical data.

0%
Cartogram
0%
Bar graph
0%
Tree chart
0%
Line polygon

Explanation

Bar graph is the graphical representation of statistical data.
Example: Here the bar graph represents the statistical profit of the year

$1992-1995$ .

A ____ graph is a chart that uses either horizontal or vertical bars to show comparisons of companies profit.

0%
line
0%
pie
0%
bar
0%
polygon

A _____ is the representation of data by using graphical symbols such as lines, bars, pie slices, histogram etc.

0%
flow chart
0%
diagram
0%
equation
0%
graph

Explanation

A graph is the representation of data by using graphical symbols such as lines, bars, pie slices, histogram etc.
Example: Line graph representing the temperature of

$8$ days.

How many more bottles of pickles were exported on Thursday than Tuesday?

0%
$1000$
0%
$1200$
0%
$1500$
0%
$2000$

Explanation

$1$ pickle jar

$= 500$ bottles
So, in the pictograph shows that more bottles of pickles were exported on Thursday than Tuesday

No. of bottles exported on Tuesday

$=5\times 500=2500$

No. of bottles exported on Thursday

$8\times 500=4000$

Thus, the more no. of bottles exported on Thursday than Tuesday

$=4000-2500 = 1500$

Find the graph used in the picture.

0%
Line graph
0%
Bar graph
0%
Polygon
0%
Pie graph

The foreign exchange reserves in 1997-98 was how many times that in 1994-95?

0%
0.7
0%
1.2
0%
1.4
0%
1.5

Explanation

Required ratio

$= \dfrac{5040}{3360} = 1.5$

Which graphs are usually scaled so that all the data can fit on the graph?

0%
Line graph
0%
Pie graph
0%
Bar graph
0%
Polyogn

The line graph shows the income of RBI department. In which of the years was the annual income the maximum?

0%
$1996$
0%
$1999$
0%
$2000$
0%
$2001$

Explanation

In graph shows the income of the RBI department was maximum in the year

$1999$ .

How many bottles did Johnson's food factory export each week?

0%
$210$
0%
$30$
0%
$105$
0%
$15,000$

Explanation

Johnson's food factory export each week

$= 30$ pickle jar

$(1$ pickle jar

$= 500)$

$= 30 \times 500 = 15,000$ bottles

The line graph shows the income of RBI department. In which of the years was the annual income the minimum?

0%
$1995$
0%
$1999$
0%
$2000$
0%
$2001$

Explanation

In graph shows the income of the RBI department was minimum in the year

$1995$ .

The frequency curve shows temperatures over

$11$ year in Bangalore. Use the graph to answer the questions below.
Which year had the lowest temperature?

0%
$2001$
0%
$2000$
0%
$2002$
0%
$2010$

Explanation

The graph shows that the lowest temperature is in the year

$2000$ .

Find the highest temperature in Bangalore over

$11$ years.

0%
$25^{o}C$
0%
$45^{o}C$
0%
$30^{o}C$
0%
$15^{o}C$

Explanation

On looking the graph, we get the highest temperature as

$45^{o}C$ in the year

$2002$ .

What is the difference in temperature between

$2003$ and

$2008$ ?

0%
$25^{o}C$
0%
$30^{o}C$
0%
$15^{o}C$
0%
$5^{o}C$

Explanation

$2003$ temperature

$=$

$30^{o}C$
In

$2008$ temperature

$=$

$25^{o}C$
So, the difference

$= 30 - 25 =$

$5^{o}C$

The frequency curve is similar to _____.

0%
histogram graph
0%
line graph
0%
bar graph
0%
pie graph

The line graph shows the number of students in each department of a school. What does the second number in the ordered pair

$(9, 10)$ represent?

0%
Number of department
0%
Line graph
0%
Number of students
0%
School department

Explanation

The second number in the ordered pair

$(9, 10)$ represent

$10$ number of students in the department

$9$ .

What is the range of temperatures in Bangalore over

$11$ years?

0%
$20^{o}C$
0%
$10^{o}C$
0%
$33^{o}C$
0%
$45^{o}C$

Explanation

Range of temperature = highest temperature

$-$ lowest temperature

$= 45 - 12 =$

$33^{o}C$
So, the range of temperatures in Bangalore over

$11$ years is

$33^{o}C$ .

How many years have temperature higher than

$35^{o}C$ ?

0%
$2$
0%
$3$
0%
$4$
0%
$5$

Explanation

Years

$2002$ and

$2005$ are having the temperature higher than

$35^{o}C$ .

Thus answer is

$2$ .

The line graph shows the number of students in each department of a school. What does the first number in the ordered pair

$(8, 30)$ represent?

0%
Number of department
0%
Line graph
0%
Number of students
0%
School department

Explanation

The first number in the ordered pair

$(8, 30)$ represent

$8$ number of departments.

In which age students do have the least number of mobile phones?

0%
$11$
0%
$12$
0%
$13$
0%
$14$

Explanation

$12$ years old students have the least number of mobile phones.

The frequency curve shows the number of students ages

$11$ through

$17$ in Chennai city that have mobile phones. Refer to the frequency curve below to answer each question.

How many mobile phones do

$13$ year-old have?

0%
$10$
0%
$15$
0%
$20$
0%
$25$

Explanation

$13$ year-old have

$15$ mobile phones as shown in the graph.

The graph above shows the student participation for

$4$ school clubs. Each student is allowed to participate in only one club. If the school has

$250$ students, calculate the number of students not in any club.

0%
$220$
0%
$90$
0%
$60$
0%
$30$

Explanation

Debate

$\rightarrow 20$ , Student council

$\rightarrow 70$ , Orchestra

$\rightarrow 90$ , choir

$\rightarrow 40$

Hence, total

$20+70+90+40=220$

Total students in the school is

$250$ .

Hence, the number of students not in any club is

$250-220=30$ .

About how many mobile phones do

$14\dfrac{1}{2}$ year old have?

0%
$20$
0%
$30$
0%
$40$
0%
$50$

Explanation

On looking the graph, we can say

$14\dfrac{1}{2}$ year old have 40 mobile phones.

The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from

$1995$ to

$2001$ .

The imports were minimum proportionate to the exports of the company in the year ?

0%
$1995$
0%
$1996$
0%
$1997$
0%
$2000$

Explanation

The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value

$0.35$ in

$1997$

Hence, the imports are minimum proportionate to the exports in

$1997$ .

At what age do students have the greatest number of mobile phones?

0%
$14$
0%
$15$
0%
$16$
0%
$17$

Explanation

At the age

$16$ , the students have the greatest number of mobile phones.

What was the least number of mobile phones at any age?

0%
$10$
0%
$15$
0%
$20$
0%
$25$

Explanation

$10$ was the least number of mobile phones at any age.

If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was ?

0%
Rs. 370 crores
0%
Rs. 320 crores
0%
Rs. 280 crores
0%
Rs. 275 crores

Explanation

Ratio of imports to exports in the year 1996 = 0.85.
Let the exports in 1996 = Rs. x crores.
Then,

$\displaystyle \frac { 272 }{ x } =0.85\Rightarrow x=\frac { 272 }{ 0.85 } =320$

$\displaystyle \therefore$ Exports in 1996 = Rs. 320 crores.

Brain and Jared live in the same apartment complex and they both bike to and from the work every day. The figure above shows a typical commute home for each of them. Based on the figure, which of the following statements is true?

0%
It takes Brain longer to bike home because his work is farther away.
0%
It takes Jared longer to bike home because his work is farther away.
0%
Jared and Brain arrive home at the same time, so they must bike at about the same rate.
0%
Jared bikes a longer distance than Brain in the same amount of time, so Jared must bike at a faster rate.

Explanation

$\Rightarrow$ In the given figure we can see Jared's distance between workplace and the apartment is more than Brain's.

$\Rightarrow$ Jared takes the same time as Brain to travel that distance.

$\therefore$ Jared bikes a longer distance than Brain in the same amount of time, so Jared must bike at a faster rate.

What is the average numbers of vehicles manufactured by Company X over the given period ? (rounded off to nearest integer)

0%
$119333$
0%
$113666$
0%
$112778$
0%
$111223$

Explanation

Average number of vehicles manufactured by Company X

$\displaystyle =\frac { 1 }{ 6 } \times \left( 119000+99000+141000+78000+120000+159000 \right)$

$\displaystyle =119333$

If the total number of candidates appeared in 1996 and 1997 together was 47400, then the total number of candidates qualified in these two years together was?

0%
34700
0%
32100
0%
31500
0%
Data inadequate

CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 2 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 2 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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