Statistics & Probability

Measures of Center & Spread

Describing a data set's center (mean, median) and spread (range, interquartile range).

Intermediate15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Statistical Questions

More Than Just an Average

Two basketball players each average exactly 15 points per game. Before reading on, think about this: does that automatically mean they play exactly the same way, game to game? What information about each player's performance is the average completely missing?

The average — the mean — hides how consistent each player actually is. One player might score close to 15 points every single game, while the other might swing wildly between 2 points and 28 points, still averaging 15 overall. Two very different playing styles can share the exact same mean, which is exactly why a full description of data needs a measure of spread alongside a measure of center.

Definition — Measures of Center and Spread

A measure of center (like the mean or median) summarizes a typical value in a data set. A measure of spread (like the range or interquartile range) summarizes how much the data varies around that typical value.

Worked Example — Comparing Two Data Sets with the Same Mean

Player A's game scores: 14, 15, 16, 15, 15 (mean = 15). Player B's game scores: 2, 28, 5, 25, 15 (mean = 15). Both means are 15, but Player A's range is 16 − 14 = 2, while Player B's range is 28 − 2 = 26. Player A is far more consistent, a fact the mean alone completely hid.

Worked Example — Finding the Range and Median of a Data Set

A data set of quiz scores: 78, 85, 90, 82, 95. Sorted: 78, 82, 85, 90, 95. The median (the middle value) is 85. The range (highest minus lowest) is 95 − 78 = 17.

Tip

Always sort a data set from least to greatest before finding the median — the middle value only means something once the data is actually in order.

Common Mistakes

Reporting only a mean or median without any measure of spread, giving an incomplete picture of the data.
Report a measure of center alongside a measure of spread — the center alone can hide very different amounts of consistency or variability within the data.
Finding the median from unsorted data, picking whichever value happens to be in the middle position as originally listed.
Sort the data from least to greatest first, then find the value in the middle position — an unsorted 'middle' value is meaningless.

Key Takeaways

A measure of center summarizes a typical value; a measure of spread summarizes how much the data varies.
Two data sets can share the same mean while having very different amounts of spread.
The median requires sorting the data first; the range is the difference between the highest and lowest values.

Summary

Combining a measure of center with a measure of spread gives a fuller, more honest picture of a data set than either alone. This closes out Grade 6 mathematics — Grade 7 builds directly on these ratio, rational number, and expression foundations, deepening proportional reasoning and introducing probability.

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