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Measures Of Dispersion

Question
CBSEENST11024409
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With an example, prove that the sum of the square of the deviations from arithmetic mean is least i.e. less than the sum of the squares of the deviations of observations taken from any other value.

Solution

a) Calculation of sum of the squares of the deviation from A.M. from an imaginary data:

X

 

(n)

(n)2

1

–2

4

2

–1

1

3

0

0

4

+ 1

1

5

+ 2

4

 

Σn2 = 10

Here, sum of the square of the deviations from A.M. is 3

... (i)

(b) Calculation of sum of the square of the deviation taken from any other value i.e. 2 (except A.M.)

X

 

(n)

(n)2

1

–1

1

2

0

0

3

+ 1

1

4

+ 2

4

5

+ 3

9

Σ

  

Σn2 = 15

Here, sum of the square of the deviation taken from any other value except A. M. is 15 ... (ii)

From (i) and (ii) we come to know that the sum of the square of the deviations from arithmetic mean is less.

Some More Questions From Measures of Dispersion Chapter

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.

How is coefficient of quartile deviation calculated?

Define mean deviation.

 

Define standard deviation.

Give formula to calculate standard deviation of a frequency destribution series by direct method.

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Mock Test Series

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