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QUESTION: 1

(Direction 1 - 21)Write down the correct answers. Each question carries one mark.

**Q. Which of the following statements is correct?**

Solution:

QUESTION: 2

Dispersion measures

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QUESTION: 3

When it comes to comparing two or more distributions we consider

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QUESTION: 4

Which one is difficult to compute?

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QUESTION: 5

Which one is an absolute measure of dispersion?

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QUESTION: 6

Which measure of dispersion is the quickest to compute?

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QUESTION: 7

Which measures of dispersions is not affected by the presence of extreme observations?

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QUESTION: 8

Which measure of dispersion is based on the absolute deviations only?

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QUESTION: 9

Which measure is based on only the central fifty percent of the observations?

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QUESTION: 10

Which measure of dispersion is based on all the observations?

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QUESTION: 11

The appropriate measure of dispersions for open – end classification is

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QUESTION: 12

The most commonly used measure of dispersion is

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QUESTION: 13

Which measure of dispersion has some desirable mathematical properties?

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QUESTION: 14

If the profits of a company remains the same for the last ten months, then the standard deviation of profits for these ten months would be ?

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QUESTION: 15

Which measure of dispersion is considered for finding a pooled measure of dispersion after combining several groups?

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QUESTION: 16

A shift of origin has no impact on

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QUESTION: 17

The range of 15, 12, 10, 9, 17, 20 is

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QUESTION: 18

The standard deviation of, 10, 16, 10, 16, 10, 10, 16, 16 is

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QUESTION: 19

For any two numbers SD is always

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QUESTION: 20

If all the observations are increased by 10, then

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QUESTION: 21

If all the observations are multiplied by 2, then

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QUESTION: 22

(Dirction 22 - 40) Write down the correct answers. Each question carries two marks.

**Q. What is the coefficient of range for the following wages of 8 workers?**

**Rs.80, Rs.65, Rs.90, Rs.60, Rs.75, Rs.70, Rs.72, Rs.85.**

Solution:

QUESTION: 23

If R_{x }and R_{y} denote ranges of x and y respectively where x and y are related by 3x+2y+10=0, what would be the relation between x and y?

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QUESTION: 24

What is the coefficient of range for the following distribution?

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QUESTION: 25

If the range of x is 2, what would be the range of –3x +50?

Solution:

Substituing x=2 in -3x+50

-3x+50=-3(2)+50

=-6+50

=44

Thus the range of -3x+50 is 44

QUESTION: 26

What is the value of mean deviation about mean for the following numbers?

5, 8, 6, 3, 4.

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QUESTION: 27

Median in set 6, 4, 2, 3, 4, 5, 5, 4 would be

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QUESTION: 28

The coefficient of mean deviation about mean for the first 9 natural numbers is

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QUESTION: 29

If the relation between x and y is 5y–3x = 10 and the mean deviation about mean for x is 12, then the mean deviation of y about mean is

Solution:

5y-3x=10

x=12

5y-3×12=10

5y-36=10

5y=46

y=46/5

y=9.2

QUESTION: 30

If two variables x and y are related by 2x + 3y –7 =0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y about mean is

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QUESTION: 31

The mean deviation about mode for the numbers 4/11,6/11,8/11,9/11,12/11,8/11 is 1/6?

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QUESTION: 32

If mean of percentages, rates and ratios is to be calculated then central tendency measure which must be used in this situation is

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QUESTION: 33

If the mean and SD of x are a and b respectively, then the SD of is

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QUESTION: 34

What is the coefficient of variation of the following numbers?

53, 52, 61, 60, 64.

Solution:

The coefficient of variation of the following numbers 53,52,61,60,64 are,

Step 1:

To find the mean of the above numbers,

x = 53+52+61+60+64 / 5 = 290/5 = 58

Step 2:

To find Standard deviation.,

S = √53² +52²+61²+60²+64² / 5 - (58²)

=√16390/5 -3364 = √3386-3364

=√22 = 4.69

Step 3 :

To find Coefficient of variation,

Coefficient of variation ( C. V) = ( S / X ) * 100

= ( 4.69 /58 ) * 100 = 0.0809 * 100

⇒8.09

QUESTION: 35

If the SD of x is 3, what us the variance of (5–2x)?

Solution:

QUESTION: 36

If x and y are related by 2x+3y+4 = 0 and SD of x is 6, then SD of y is

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QUESTION: 37

The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is

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QUESTION: 38

If x and y are related as 3x+4y = 20 and the quartile deviation of x is 12, then the quartile deviation of y is

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QUESTION: 39

If the SD of the 1st n natural numbers is 2, then the value of n must be

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QUESTION: 40

If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation is

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