11.4 Measures of Dispersion

11.4 Measures of Dispersion

The following data shows the runs scored by two batsmen in the last 10 matches: Batsman A: 25, 20, 45, 93, 8, 14, 32, 87, 72, 24 Batsman B: 33, 50, 47, 38, 45, 40, 36, 48, 37, 46 Mean of Batsman A = $\frac{25 + 20 + 45 + 93 + 8 + 14 + 32 + 87 + 72 + 24}{10} = \frac{420}{10} = 42$ Mean of Batsman B = $\frac{33 + 50 + 47 + 38 + 45 + 40 + 36 + 48 + 37 + 46}{10} = \frac{420}{10} = 42$

Batsman A

[Fig. Batsman A]

Batsman B

[Fig. Batsman B]

Although both batsmen have the same mean score, batsman $B$'s runs are closely clustered around the mean, while batsman $A$'s scores are widely spread from 0 to 100. Therefore, to understand how the data values are spread out, we need more statistical information. For this purpose, we will study measures of dispersion. Measures of dispersion are statistical tools used to describe how spread out or scattered the values in a data set are around a central value. Different measures of dispersion are

1. Range 2. Variance 3. Standard deviation
2. Interquartile range 5. Mean deviation 6. Quartile deviation
3. Coefficient of Variations In this unit, we will discuss only a few measures of dispersion.