the reasons behind the computation of measures of dispersions?

Question

the reasons behind the computation of measures of dispersions

Answer 1

standard deviation is a measure of dispersion of a set of values from the mean.

for. e.g the set of numbers 1, 2, 198, 199 has the mean 100
So does the set 98, 99, 101, 102.

But is the mean representative of the values in the set??
Most defnitely not for the first set and definitely yes for the second. So a mean is not enough to represent the values in a set through a single number. This is the motivation for defining a number known as the standard deviation. It is defined as the root mean square of the deviations of all numbers in the set from their mean.

The standard deviation for the first set is thus large and for the second is quite small implying the numbers in the first set have widely varying values and the numbers in the second are close by and are aptly represented by their mean.

Answer 2

The purpose of measures of dispersion is to find out how spread out the data values are on the number line. Another term for these statistics is measures of spread.

Simply it answers the question how much the data is dispersed. Through it we can develop an idea about reliability of data