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Measures Of Dispersion

Question
CBSEENST11024845
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Prove that mean deviation is based on all values. A change in even one value will effect of.

Solution

In order to prove the statement given in the question, we calculate the mean deviation of the following data : 2, 4, 7, 8, 9.

X

D

2

4

4

2

7

1

8

2

9

3

ΣX = 30

ΣD = 12

Now change one value i.e. we take 14 in place of 9.

X

D

2

5

4

3

7

0

8

1

14

7

ΣX = 35

ΣD = 16

In this way we see that mean deviation changes with a change in even one value. Earlier, the mean deviation was 2.4. After the change in one value it is 3.2.

Some More Questions From Measures of Dispersion Chapter

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.

 

Define quartile deviation.

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