# Measures of Dispersion

Dispersion may be defined as the extent of the scatteredness of item around a measure of central tendency.

# Methods of measuring dispersion

The following are the methods of measuring dispersion: (i) the range; (ii) the semi-interquartile range or quartile deviation; (iii) the mean deviation; and (iv) the standard deviation.

Range

It is the difference between the highest and the lowest value in the series, i.e., Range = xh - xl, where xh is highest value and xl is the lowest value. The coefficient of range = (xh - xl)/(xh + xl).

# Mean deviation

Individual series
MD =

where M = median/mean/mode, n = number of observations.

Discrete series
MD =

Note: In general, mean deviation (MD) always stands for mean deviation about the median.

# Standard deviation

The arithmetic mean of the square of deviations of the variable values from its actual arithmetic mean is known as variance and its square root is known as standard deviation (Ïƒ).

Individual series
Ïƒ2 = variance =

Discrete series
Ïƒ2 = variance =

Standard deviation
(Ïƒ) =

Note: If di =  then
Ïƒ2 = h2