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Measures Of Dispersion

Question
CBSEENST11024374
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Briefly explain the various measures calculated from standard deviation.

Solution

Measures calculated from standard deviation :

Mainly following measures are calculated from standard deviation :

1. Coefficient of standard deviation : It is a relative measure of standard deviation. It is calculated to compare the variability in two or more than two series. It is calculated by dividing the standard deviation by arithmetic mean of data symbolically.

2. Coefficient of Variance : It is most propularly used to measure relative variation of two or more than two series. It shows the relationship between the S.D. and the arithmetic mean expressed in terms of percentage. It is used to compare uniformly, consistency and variability in two different series.

3. Variance : It is the square of standard deviation. It is closely related to standard deviation. It is the average squared deviation from mean where as standard deviation is the square is the square root of variance. Symbolically

Some More Questions From Measures of Dispersion Chapter

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?

Define range.

 

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