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Measures Of Dispersion

Question
CBSEENST11024828
Wired Faculty App

What are the four alternative measures of absolute dispersion ? Discuss their properties.

Solution

The four alternative measure of absolute dispersion are:

(i) Range, (ii) Quartile Deviation, (iii) Mean deviation, (iv) Standard Deviation.

1. Features of the range :

(a) It is rigidly defined.

(b) It is easy to calculate and simple to interpret.

(c) It does not depend on all values of the variables.

(d) It is unduly affected by extreme values.

(e) The range depends on the units of measurement of the variable.

2. Features of Quartile deviation :

(a) It is rigidly defined.

(b) It is easy to calculate and simple to interpret.

(c) It does not depend on all values of the variable.

(d) The units of measurement of the quartile deviation are the same as those of the variable.

3. Features of mean deviation :

(a) It is rigidly defined.

(b) It depends on all values of the variable.

(c) It is based on absolute deviations from a central values.

(d) It is easy to understand.

(e) It involves harder calculations than the range and quartile deviation.

(f) It is amendable to algebraic treatment.

(g) The units of measurement of the mean deviation are the same as those of the variable.

4. Features of Standard deviation :

(a) It is the best measure of the variation because it is based every item of the series and further algebraic treatment is possible.

(b) It is not very much affected by fluctuation of sampling.

(c) It is the only measure for calculating combined standard deviation of two or more graphs.

(d) It is a definite measure of dispersion.

Some More Questions From Measures of Dispersion Chapter

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.

How is coefficient of quartile deviation calculated?

Define mean deviation.

 

Define standard deviation.

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