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Measures Of Dispersion

Question
CBSEENST11024390
Wired Faculty App

The Standard deviation of height measured in inches will be larger than the Standard Deviation of heights measured in foot for the same group of individuals. Comment on the validity or otherwise of this statement with appropriate explanation.

Solution

The statement given in the question is absolutely correct. The reason is that standard deviation is an absolute measure. It can create problem when units of measurement are different. The lesser the measurement the higher the standard deviation and vice-versa. If we measure the height in inches the instead of foot, than the S.D. will increase 12 times. It has been explained below with an example.

Suppose we are given the height of 5 good in foot in the following table. With the help of the table, we will calculate S.D.

Height in foot (X)

D

D2

2

–4

16

4

–2

4

6

0

0

8

2

4

10

4

16

ΣX = 30

  

ΣD2 = 40

Now we will calculate S.D. taking the height of 5 same persons in inches.

Height in inches (X)

D

D2

24

–48

2304

48

–24

576

72

0

0

96

+24

576

120

+48

2304

ΣX = 360

  

ΣD2 = 5760

Hence, it is proved that the deviation of height measured in inches will be larger than heights measured in foot.

Some More Questions From Measures of Dispersion Chapter

Which measure of dispersion is the best and how?

Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?

In a town 25% of the persons earned more than Rs. 45000, whereas 75% earned more than Rs. 18000. Calculate the absolute and relative values of dispersion.

A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:

X

Y

25

50

85

70

40

65

80

45

120

80

Which batsman should be selected if we want

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.

Life (in hrs)

No. of bulbs

Brand A

Brand B

0–50

15

2

50–100

20

8

100–150

18

60

150–200

25

25

200–250

22

5
 

100

100

(i) Which brand gives higher life?

(ii) Which brand is more dependable?

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution:

Classes

Frequencies

20–40

3

40–80

6

80–100

20

100–120

12

120–140

9
 

50

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