Median Calculator

The median is the middle value of a data set once every number has been arranged in order from smallest to largest. Unlike the mean, which is calculated using every value in a formula, the median only cares about position: it is whichever number sits exactly in the middle of the sorted list. If there is an even number of values, there is no single middle number, so the median is defined as the average of the two values closest to the middle. To find a median by hand, first sort the list. If you have 5, 3, 9, 1, 7, sorting gives 1, 3, 5, 7, 9. With five values (an odd count), the middle position is the third number, which is 5. That is your median. Now suppose you have six values: 1, 3, 5, 7, 9, 11. There is no single middle number, so you average the two values sitting in positions three and four, which are 5 and 7. Their average is 6, so the median is 6. Why does the median matter? Because it is resistant to outliers in a way the mean is not. Go back to the salary example: five employees earning £30,000, £31,000, £32,000, £35,000, and £500,000. Sorted, the middle value (position three) is £32,000. That single number is a far better description of what a "typical" employee earns than the mean of £125,600, which is dragged upward by one unusually high salary. This is exactly why household income statistics, home prices, and similar figures are almost always reported as medians in the news rather than means — a handful of very wealthy households or very expensive properties would otherwise distort the picture. A common misconception is that the median is always close to the mean. That is only true for roughly symmetric data. For skewed data — where a few values are far larger (or smaller) than the rest — the mean and median can diverge substantially, and the gap between them is itself a useful signal: a big gap tells you your data has significant outliers or a heavy tail in one direction. Another misunderstanding is about the even-count case. Some people assume you just pick "one of the two middle numbers," but the correct definition always averages them. If your two middle values are 4 and 10, the median is 7, not 4 or 10. This calculator handles that automatically and also shows you the full sorted list, so you can see exactly which two numbers were averaged (or which single number was chosen, in the odd case) rather than trusting a black box. The median pairs naturally with the mean and mode. Comparing all three, alongside the standard deviation and range, gives a much richer picture of a data set than any single statistic alone — which is exactly what the companion Statistics Calculator on this site computes in one pass.