rectangles are of equal lengths

rectangles are drawn with unequal shapes between them

width of rectangles carry important meaning

MCQ Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 1

To prevent frauds in multiple mortgage cases, under SARFAESI Act, 2002, one special thing has been created and made operative from 01-04-Which one is that from the following?

0%
Special Register Office at Lucknow
0%
Special Central Arbitration Bureau at Lucknow
0%
Central SARFAESI Tribunals at six centres
0%
Central Electronic Registry

$\sum _{ i=1 }^{ 18 }{ }$

$(X_{i}-8)=9$ and

$\sum _{ i=1 }^{ 18 }{ }$

$(x_{i}-8)^{2}=45$ , then the standard deviation of

$x_{1},x_{2},.....,x_{18}$ is

0%
4/9
0%
9/4
0%
3/2
0%
2/3

$b_{i} = 1 - a_{i}, na = \displaystyle \sum_{i = 1}^{n} a_{i}, nb = \displaystyle \sum_{i = 1}^{n}b$ , then

$\displaystyle \sum_{i = 1}^{n}a_{i}b_{i} + \displaystyle \sum_{i = 1}^{n} (a_{i} - a)^{2} =$

0%
$ab$
0%
$-nab$
0%
$(n + 1)ab$
0%
$nab$

Tabulation of data makes the presentation of facts and figures ___________.

0%
more simplified
0%
more understandable
0%
Both a&b
0%
It is lengthy and occupies space

Two distributions each of

$5$ observations having veriance

$4$ and

$5$ . If their arithmetic mean are

$2$ and

$4$ respectively., Find the variance of combined distribution

0%
$5/2$
0%
$11/2$
0%
$6$
0%
$13/2$

Two sets each of

$20$ observations, have the same standard deviation

$'5'$ . The first set has a mean

$'17'$ and the second set mean

$'22'$ then standard deviation of the combining the given two sets is

0%
$4.49$
0%
$5.59$
0%
$6.49$
0%
$7.59$

The standard deviation of a varibale x is

$\sigma$ . The standard devaition of the varibale

$\frac { ax+b }{ c }$ where a, b, c are constant is _____________________.

0%
$\left( \frac { a }{ b } \right) \sigma$
0%
$\left| \frac { a }{ c } \right| \sigma$
0%
$\left| \frac { a^{ 2 } }{ c^{ 2 } } \right| \sigma$
0%
$(a)\sigma$

Consider the first

$10$ positive integers. If we multiply each number by

$-1$ and then add

$1$ to each number, the variance of the numbers so obtained is

0%
$8.25$
0%
$6.5$
0%
$3.87$
0%
$2.87$

If 25% of the items are less than 10 and 25% are more than 40, then the coefficient of quartile deviation is

0%
30
0%
50
0%
1.2
0%
0.6

The standard deviation of

$50$ values of a variable x is

$15$ ; if each value of the variable is divided by

$(-3)$ ; then the standard division of the new set of

$50$ values of x will be

0%
$15$
0%
$-15$
0%
$5$
0%
$-5$

The quartile deviation of wages is

0%
$22.5$
0%
$25$
0%
$20$
0%
$21.2$

$\sum _{ i=1 }^{ 9 }{ ({ x }_{ i }-5)=9 }$ and

$\sum _{ i=1 }^{ 9 }{ { { ( }x_{ i }-5 })^{ 2 }=45 },$ then the standard deviation of the 9 items

${ x }_{ 1 },{ x }_{ 2, }.........{ x }_{ 9 }$ is

0%
4
0%
2
0%
3
0%
9

Variance can be calculated using:

0%
${\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$
0%
$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)}{n}\right)}$
0%
$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)}$
0%
$\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)$

Explanation

Variance gives the degree to which the numerical data tend to spread about the value.

Variance is given by

$\dfrac{\sum x^2}{n}-(\dfrac{\sum x}{n})^2$

2 weeks

0%
$7cm$
0%
$8cm$
0%
$9cm$
0%
$10cm$

Explanation

In the given graph, The straight line represents the growth of the Plant

$B$ .

From the graph, we can observe that after

$2$ weeks Plant

$B$ has grown

$7\space cm$

Marks scored by Rishi in an examination (out of

$100$ marks) in different subjects are shown by the bar graph given above. In which subject Rishi is best?

0%
Physics
0%
Biology
0%
English
0%
Computers

Quartile deviation for a frequency distribution is given by

0%
$Q=\cfrac { 1 }{ 4 } (Q_{ 2 }-{ Q }_{ 1 })$
0%
$Q=\cfrac { 1 }{ 3 } (Q_{ 3 }-{ Q }_{ 1 })$
0%
$Q=\cfrac { 1 }{ 2 } (Q_{ 3 }-{ Q }_{ 1 })$
0%
$Q=(Q_{ 3 }-{ Q }_{ 1 })$

Explanation

It is fundamental concept that quartile deviation of any frequency distribution is given by,

$Q = \cfrac{1}{2}(Q_3-Q_1)$

To compare the relative growth or decline of two or more series the most appropriate chart to be drawn would be

0%
line
0%
bar
0%
ratio
0%
multiple

In a bar chart:

0%
rectangles are of equal lengths
0%
width of rectangles is fixed
0%
rectangles are drawn with unequal shapes between them
0%
width of rectangles carry important meaning

The following line graph shows the yearly sales figures for a manufacturing company. Compute the difference between the sales (in Rs. crores) in

$2002$ and

$2006$ .

0%
$4$
0%
$6$
0%
$7$
0%
$10$

Explanation

From the graph the value on

$y$ - axis (denoting sales) for the year

$2002$ is Rs

$4$ crore.
From the graph the value on

$y$ - axis (denoting sales) for the year

$2006$ is Rs

$8$ crore.
Difference in sales

$= 8 - 4$ =

$4$ crore.

The patient's temperature was same for two times during the period given. These two times were:

0%
1 pm and 2 pm
0%
2 pm and 3 pm
0%
12 noon and 3 pm
0%
9 am and 10 pm

The following line graph shows the yearly sales figures for a manufacturing company. What were the sales in

$2005$ ?

0%
$4$
0%
$6$
0%
$7$
0%
$10$

Explanation

From the graph the value on

$y - axis$ (denoting sales) for the year

$2005$ is Rs.

$10$ crore

The following line graph shows the yearly sales figures for a manufacturing company. What were the sales (in Rs. crores) in

$2002$ ?

0%
$2$
0%
$4$
0%
$6$
0%
$8$

Explanation

As shown in the above graph,

$y$ axis represents the sales(in crores) and

$x$ axis represents the years.

So in the year

$2002$ the sales were upto

$4$ crore.

_____ represents data that changes continuously over period of time.

0%
Line graph
0%
Pie graph
0%
Bar graph
0%
Histogram

The variance is the _______ of the standard deviation.

0%
Square
0%
Cube
0%
Square root
0%
Cube root

The following line graph shows the yearly sales figures for a manufacturing company. What were the sales (in Rs. crores) in

$2006$ ?

0%
$2$
0%
$4$
0%
$6$
0%
$8$

Explanation

From the graph the value on

$y - axis$ (denoting sales) for the year

$2006$ is Rs

$8$ crore

The following line graph shows the yearly sales figures for a manufacturing company. What were the sales (in Rs. crores) in

$2003$ ?

0%
$6$
0%
$7$
0%
$8$
0%
$10$

Explanation

From the graph the value on

$y - axis$ (denoting sales) for the year

$2003$ is Rs

$7$ crore

Draw a graph for the following:

Side of square (in cm)	2	3	4	5	6
Area (in cm $^2$ )	4	9	16	25	36

Is the graph linear?

0%
Yes
0%
No
0%
Cannot be determined
0%
None of these

Which of the following are types of graph which include bars?

0%
Bar graph
0%
Pie graph
0%
Histogram
0%
Line graph

Which one of the following statements is correct ?

0%
Th Standard deviation for a given distribution is the square of the 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 half of the variance.

Explanation

We know

$Variance(\sigma^2)=\dfrac{\sum(x-\overline{x})^2}{n}$

Where,

$\sigma^2$ is variance

$\overline{x}$ is mean

$n$ is number of observations.

Standard deviation

$(\sigma)=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$

$\therefore$ We can see, the standard deviation for a given distribution is the square root of the variance.

The measure of dispersion is

0%
M.D.
0%
S.D.
0%
Q.D.
0%
All of these

Marks scored by Rishi in an examination (out of

$100$ marks) in different subjects are shown by the bar graph given below. The ratio of the highest marks to the lowest marks is

0%
$4:3$
0%
$3:4$
0%
$9:16$
0%
$12:9$

Explanation

Highest marks

$= 80$
Lowest marks

$=60$

Ratio

$= \dfrac{80}{60} = \dfrac{4}{3}$

Marks scored by Rishi in an examination (out of

$100$ marks) in different subjects are shown by the bar graph given above. Percentage of marks obtained is around

$70$ in which of the following subjects.

0%
Maths
0%
English
0%
Biology
0%
Computers

Explanation

From the bar graph shown in the figure, it can be seen that the marks in English and Computer lie between the scale of 60 and 80.

However, the marks scored in Computer tend to appear

$70$ from the bar-graph.

Thus the correct option is D.

If 25% of the observations in a frequency distribution are less than

$20$ and 25% are more than

$40$ , then the quartile deviation is

0%
20
0%
30
0%
40
0%
10

Explanation

Here

$Q_1 = 20, Q_3 = 40$
Hence quartile deviation of the given frequency distribution is

$=\cfrac{1}{2}(Q_3-Q_1)=10$

Quartile deviation is :

0%
$\cfrac { 4 }{ 5 } \sigma$
0%
$\cfrac { 3 }{ 2 } \sigma$
0%
$\cfrac { 2 }{ 3} \sigma$
0%
$\cfrac { 5 }{ 4 } \sigma$

Explanation

It is fundamental concept that for moderately skewed distribution

$Q.D = \cfrac{2}{3}\sigma$

The median of a symmetrical distribution, whose lower and upper quartiles are 60 and 80 respectively, is

0%
60
0%
80
0%
70
0%
None of these

Explanation

Given, lower quartile

$=60$ and upper quartile

$=80$

$\therefore$ median

$=\frac{\mbox{ lower quartile }+\mbox{ upper quartile }}{2}=\dfrac{60+80}{2}=70$

A graph drawn using vertical bars is called

0%
bar graph
0%
line graph
0%
pictograph
0%
pie graph

$\Uparrow \quad \Uparrow\quad \Uparrow \quad \Uparrow$ Number represented by figure is ____, if each symbol represents 5 houses.

0%
$4$
0%
$20$
0%
$5$
0%
$40$

Explanation

Answer:- one

$\Uparrow$ represents

$5$ houses.

There are total

$4$ such symbols .

$\therefore \Uparrow \Uparrow \Uparrow \Uparrow \; represents \;4\times 5=20$

$20$

0%
$6$
0%
$10$
0%
$12$
0%
$26$

Explanation

$\Rightarrow$

$\square\,\square\,\square\,\square\,\square\,\square$ stands for

$30.$

$\Rightarrow$

$6$ squares stands for

$30$

$\Rightarrow$

$1$ square

$=\dfrac{30}{6}=5$

$\therefore$

$\square=5$

$\Rightarrow$

$\square\,\square=2\times 5=10$

$\therefore$

$\square\,\square$ stands for

$10$

Study the graph below showing the position of 3 runners, Pooja, Mayur and Hemant at two different times.
Who has run the fastest in between the 2nd and the 4th minute?

0%
Pooja
0%
Mayur
0%
Hemant
0%
Both Pooja and Hemant

On which day the bus was most crowded?

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

Which of the following statements is not correct for a bar graph?

0%
All bars have different thickness
0%
Distance between two consecutive bars is the same
0%
The bars can touch each other
0%
The thickness has no significance

Explanation

Statement

$A$ is false as a bar graph has bars of uniform thickness.

The pictograph below shows the amount of money each class raised for an animal shelter

0%
Rs. $10$
0%
Rs. $40$
0%
Rs. $50$
0%
Rs. $100$

Explanation

If class iv raised

$200$ ,

then each

$\lozenge$ =

$\frac{200}{4}$ =

$Rs50$

$\therefore$ Amount money raised each class is

$50$

The given line graph shows the growth rate of a kitten During which

$2$ month period the kittens weight increased the most

0%
$0$ to $2$ months
0%
$2$ to $4$ months
0%
$4$ to $6$ months
0%
$6$ to $8$ months

Explanation

The line graph shown is steepest from the period of

$2$ months to

$4$ months showing that the growth is maximum

If O represents

$5$ eggs then how many eggs does OOOO represent?

0%
$4$
0%
$16$
0%
$20$
0%
$25$

Explanation

Given, O represents

$5$ eggs eggs

$\therefore$ OOOO represents

$5\times 4 =20$ eggs.

The population of four towns

$A, B, C$ and

$D$ as in

$2011$ are as follows:

Town	Population
$A$	$6863$
$B$	$519$
$C$	$12185$
$D$	$1755$

What is the most appropriate diagram to present the above data ?

0%
Pie chart
0%
Bar chart
0%
Histogram
0%
Line graph

Explanation

Since, there are only two variables (Town and Population) and only

$4$ data points. Thus, a bar graph can be used to compare the population in the four towns.

Number of TV sets sold in the year

$1995$ is

0%
$1000$
0%
$500$
0%
$50$
0%
$2000$

Explanation

$1995=\square\times 1$

Each

$\square=500$ TV sets

$1995$ no. of TV sold

$=500$

0%
$5$
0%
$50$
0%
$6$
0%
$60$

Explanation

Given that one man symbol represents

$12$ men.

Therefore,

$5$ symbols represents

$12\times 5=60$ men.

A graph drawn using vertical bars is called

0%
Bar graph
0%
Line graph
0%
Pictograph
0%
Pie graph

Variance of the distribution

$73, 77, 81, 85,..., 113$ is

0%
$10$
0%
$160$
0%
$161$
0%
None of these

Explanation

$73,77,81...113$ are in A.P

where

$a=73,d=4$

$\therefore 113=a+\left( n-1 \right) d\Rightarrow 113=73+\left( n-1 \right) 4\\ \Rightarrow 40=\left( n-1 \right) 4\Rightarrow 10=n-1\Rightarrow n=11$

$\displaystyle S=\frac { 11 }{ 2 } \left( 73+113 \right) =1023$

$\displaystyle \overline { x } =\frac { 1023 }{ 11 } =93$

Therefore variance

$\displaystyle \frac { \sum { { \left( x-\overline { x } \right) }^{ 2 } } }{ N } =161$

Number of TV sets sold in the year 1980 is

0%
1000
0%
1500
0%
1250
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

No. of TV sets sold in year 1980 = 1000

A) 1000

CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 1 - 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 1 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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