Spread in data — Data, 14–17 years
How far apart values are, not just where their centre lies. Data, 14–17 years.
The idea
Spread describes how much the values differ from one another. The range is the largest value minus the smallest, while the interquartile range covers the middle half of the data. Two groups can share the same mean but have very different spread: one may be consistent and the other highly varied.
Why we need it
A centre alone cannot tell whether results are tightly grouped or far apart. This matters whenever reliability, risk or fairness matters: an average journey time of 20 minutes could mean nearly every trip takes 20 minutes, or that half take 5 and half take 35. Spread adds the missing sense of consistency.
Worked example
For the scores 6, 7, 8, 9 and 15, the range is 15 − 6 = 9 points. To find the middle-half spread, split the ordered data around the median 8: the lower half is 6, 7 and the upper half is 9, 15. Their middle values are 6.5 and 12, so the interquartile range is 12 − 6.5 = 5.5 points.
The common trap
A common mistake is to compare means and ignore spread, because one headline number is quicker to read. Another is to use the range as if it always tells the whole story. Both are understandable: the range is simple, but one outlier can control it. Check a graph or a second measure before deciding how consistent the data are.
Where it is used
Manufacturers monitor spread in the size of parts, because inconsistent parts may not fit together. Investors and insurers study variation in prices or losses, not just their average. In sport, two athletes with the same average time may differ greatly in consistency. Spread helps decide whether a result is dependable enough for a real choice.
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