Measures Of Dispersion

Question

Wired Faculty App

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?

Solution

Increase in each worker wages = Rs. 20

Total increase in wages = 50 × 20 = Rs. 1000

Total of wages before increase worker in wages = 50 × 200 = Rs. 10,000

Total wages after increase in wages

Hence, mean wages will be affected but standard deviation will not be affected as the standard deviation is independent of origin. Have the wages become or less uniform? In order to calculate uniformity wages, we will have to calculate co-efficient of variation.

Afterwards

Now more uniformity in wages has taken place.

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?