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Measures Of Dispersion

Question
CBSEENST11024363
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The following table gives you the height of 100 persons. Calculate dispersion by range method.

Height in Centimetres

No. of Persons

Below 162

2

Below 163

8

Below 164

19

Below 165

32

Below 166

45

Below 167

58

Below 168

85

Below 169

93

Below 170

100

Solution

Calculation of dispersion by Range method:

Height in Centimetres

No. of Persons

161–162

2

162–163

6

163–164

11

164–165

13

165–166

13

166–167

13

167–168

27

168–169

8

169–170

7

Total

100

Some More Questions From Measures of Dispersion Chapter

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

A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment

Define dispersion.

How many methods are there to calculate dipersion?

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