. Measures of Dispersion The following data provide the runs scored by two batsmen in the last matches. Batsman A: , , , , , , , , , Batsman B: , , , , , , , , , Mean of Batsman A = = Mean of Batsman B = = The mean of both datas are same ( ), but they differ significantly. No.
of Matches Fig. . (a) Batsman A Runs No. of Matches Fig.
. (b) Batsman B Runs From the above diagrams, we see that runs of batsman B are grouped around the mean. But the runs of batsman A are scattered from to , though they both have same mean. Thus, some additional statistical information may be required to determine how the values are spread in data.
For this, we shall discuss Measures of Dispersion . Dispersion is a measure which gives an idea about the scatteredness of the values. Measures of Variation (or) Dispersion of a data provide an idea of how observations spread out (or) scattered throughout the data. Different Measures of Dispersion are .
Range . Mean deviation . Quartile deviation . Standard deviation .
Variance . Coefficient of Variation . . Range The difference between the largest value and the smallest value is called Range.
Range R = L– S Coefficient of range = L S L S where L - Largest value; S - Smallest value Example . Find the range and coefficient of range of the following data: , , , , , , . Solution Largest value L = ; Smallest