# 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 =

*x*_{h}*-**x**, where*_{l}*x*is highest value and_{h}*x**is the lowest value. The coefficient of range = (*_{l}*x*_{h}*-**x**)/(*_{l}*x*+_{h}*x**).*_{l}# 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**

Ïƒ

^{2}= variance ==

**Discrete series**

Ïƒ

^{2}= variance ==

**Standard deviation**

(Ïƒ) =

**If**

*Note:**d*= then

_{i}Ïƒ

^{2}=*h*^{2}