How spread out data is — Data, 11–13 years
Two data sets can have the same average but very different amounts of variation. The range, found by subtracting the smallest value from the largest, gives a quick first measure of spread.
Spread shows the variation
A centre tells you where the data is gathered, but spread tells you how far apart the values are. The range is the distance from the smallest value to the largest value. A larger range means the data reaches across a wider interval.
Why spread matters
An average alone can hide an important difference. Two teams might both score 10 points on average, but one may score nearly 10 every time while the other swings between 2 and 18. Spread helps us notice how predictable the results are.
Calculating a range
A runner records 12, 15, 15, 18 and 22 minutes. The smallest time is 12 and the largest is 22. Subtract: 22 − 12 = 10 minutes, so the range is 10 minutes. It describes the full width of these results.
Range is not an average
It is easy to read a range of 10 as if the typical result were 10. That is reasonable because both the mean and the range are single numbers, but the range is a difference between two extremes, not a result that anyone necessarily achieved.
Spread in real decisions
A weather service can compare the range of temperatures in two weeks, not just their average. A smaller range may mean steadier weather, while a larger one warns that clothing or travel plans may need to change.
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