Measures of Dispersion

Consider  the following sets of data,

Set 1: 1, 3, 4, 24, 32, 26, 58, 92

Set 2: 28,29,30, 30, 32, 31,27,33. Suppose these are the marks of two groups of students.  When we compare the two groups based on mean, we will arrive at the conclusion that both groups are equal in their performance. But it is clear from the raw data itself that the two groups are not equal in their performance. In the first case, there are extreme values but in the second set all values are almost equal. This example shows the inadequacy of measures of central tendency in comparing the sets of data. Together with measures of central tendency if the scatteredness of the values from the central value is considered, the comparison will be more accurate. Therefore we need to calculate the measure of scatteredness or dispersion of the values in a distribution. That is measures of central tendency will give a value that represent the entire distribution, but do not show how the individual scores are ‘spread’ or ‘scattered’, which is very important in cases where we have to describe and compare two or more frequency distributions or sets of scores.

The measure of dispersion gives the degree of variability or dispersion, which is an index of  how the individual scores are scattered or spread throughout the data. Mainly used measures of dispersion are Range, Quartile Deviation, Mean Deviation, and Standard Deviation.