Mean, Median and Mode

Four summaries, four questions

Paste 1, 2, 2, 3, 100. The mean is 21.6 because 100 is in the sum. The median is 2 — the middle of the sorted list. The mode is 2, the value that appears twice. The range is 99. None of those four numbers is “the” average; each answers a different sentence. The mean, median, mode and range calculator reports all four from one paste so you can see when they disagree.

The average calculator is only the arithmetic mean, plus count and sum. Use it when the question is literally “mean of this list.” Switch pages when you also need the middle or the most common value.

When the mean is a poor typical

Household income, house prices and session times are the usual classroom examples: a few large values drag the mean up while most rows sit near the median. Reporting only the mean then sounds like “typical” when it is closer to “total divided by count.” The median ignores how far the tail goes; that is a feature when you want a resistant centre, and a flaw when the tail is the story (total rainfall, total spend).

Even counts and empty modes

An even-length list has no single middle row. The usual rule — and this site’s — is to average the two central values after sorting. Mode is about frequency, not position: 7, 7, 8, 9, 9 has two modes. A list with all unique values has no unique mode; the page should say so rather than invent a favourite.

Spread is a different tool

Range is only max − min. Two lists can share a mean and a median and still be tight or wild. Variance and both standard deviations live on the statistics calculator. Sample versus population is a choice of denominator there, not a guess this four-number page makes.