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Mathematics · Ch 7 — Statistics

Range

7.3

Range

Range – The Simplest Measure of Dispersion

When we look at two sets of data, the first thing we often notice is how spread out the numbers are. In the example of batsmen A and B, we saw that A’s scores ranged from 0 to 117, while B’s scores were all between 46 and 60. That single observation — the gap between the smallest and largest value — already tells us something important about variability.

The range of a data set is defined as the difference between the maximum value and the minimum value.

Range=Maximum value−Minimum value\text{Range} = \text{Maximum value} - \text{Minimum value}

For batsman A, the range is 117−0=117117 - 0 = 117. For batsman B, the range is 60−46=1460 - 46 = 14. Since 117>14117 > 14, we say that A’s scores are more scattered or dispersed than B’s scores, which are clustered closely together.

Note

The range gives only a rough idea of variability. It depends entirely on just two extreme values — the largest and the smallest — and ignores everything in between. Two data sets can have the same range but very different distributions.

Why Range Is Not Enough

The range tells us the total spread of the data, but it does not tell us how the data are spread around a central value like the mean or median. For example, consider these two sets:

  • Set X: 10, 20, 30, 40, 50 — range = 40
  • Set Y: 10, 10, 50, 50, 50 — range = 40

Both have the same range, but the pattern of dispersion is completely different. In set X, the values are evenly spaced; in set Y, they are bunched at the extremes. The range cannot capture this difference. …

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