Average Calculator

The mean is the balancing point of the data: if the values were weights on a ruler, it is where the ruler balances. It uses every value, which makes it efficient and also makes it vulnerable — one extreme number drags it.

The median is the middle of the sorted list. Half the data is above it, half below. It ignores how far away the extremes are, so it survives outliers intact. This is why income, house prices and response times are almost always reported as medians.

The mode is the most common value. It is the only average that works on categories rather than numbers, and the only one that can be plural — a data set can have two or more modes, or none at all.

The range is not a measure of centre at all. It describes spread, using only the two most extreme observations, which makes it the least stable summary in statistics but a useful quick check for data-entry errors.

In the example above, six of seven tickets resolved in under 25 minutes, yet the mean is 27.86 — higher than all but one. Reporting "average resolution time: 28 minutes" describes no ticket that actually happened.

This is the classic failure mode of the mean, and it appears everywhere real data is skewed. Salaries in a company with one very senior executive, page-load times with a few timeouts, order values with one bulk purchase. The rule of thumb: if the mean and median differ by more than about 10–15% of the median, look at your data before quoting the mean.

With an even number of values there is no single middle, so the median is the average of the two central numbers. For 10, 20, 30, 40 the median is (20 + 30) ÷ 2 = 25 — a value that does not appear in the data, which is normal and correct.

Modes can tie. If two values both appear three times and nothing appears more often, the data is bimodal and both are reported. This calculator lists all tied modes rather than arbitrarily picking one, because a bimodal distribution usually means two different populations have been mixed together — and that is worth noticing.

The arithmetic mean is the wrong tool for some kinds of data. Rates of growth compound, so a sequence of +50% and −50% averages to 0% arithmetically but actually loses 25% — the geometric mean handles that correctly. Speeds over a fixed distance need the harmonic mean: driving out at 30 mph and back at 60 mph averages 40 mph, not 45.

And when values carry different importance — course credits, portfolio sizes, survey strata — a weighted average is required. Using a plain mean there silently treats a 1-credit course as equal to a 5-credit one.