Statistics

Measure of Dispersion

Exercise 8.1

1. a) What is dispersion ?

Solution

Dispersion

The measure of variability or the spread of the data from the central value is called dispesion.

b) Write the various measures of dispersion ?

Solution

The various measures of dispersions are:

i) Range

ii) Quartle deviation

iii) Mean deviation

iv) Standard deviation

Prepare the frequency distribution of the following data taking first class-interval of 10-20 and calculate Q.D. and its coefficient:

47, 50, 35, 28, 40, 15, 54, 61, 27, 70, 22, 30, 37, 73, 12, 48, 20, 52, 65, 33, 75, 66, 60, 22, 46, 58, 14, 43

Soln: From the data given above preparing the frequency distribution as the first class 10-20 to find the quartile deviation:

Mean Deviation

Standard deviation

The standard deviation is defined as the positive square root of the arithmetic mean of the squares of the deviations of the items taken from mean. It is denoted by Greek letter s (sigma).

Standard deviation is the best method of measuring the dispersion because

(i) its value is based on all the observation.

(ii) The deviation of each item is taken from mean.

(iii) all algebraic sign are also considered.

(iv)it gives more accurate result.

Some Important Formulae

Solved Problems

Q.1. What do you mean by standard deviation?

Sol :Standard deviation is defined as the positive square root of the arithmetic mean of the squares of the deviations of the items taken from mean. It is denoted by the Greek letter s (sigma).