Median Calculator
Median, quartiles and why it beats the mean.
Work out Median. Median, quartiles and why it beats the mean. Names the convention it used.
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Median
9
7 values · mean 10.1429 · Skewed right
The median is the middle value and the mean is the average, and the gap between them is the useful part. One extreme value drags the mean and leaves the median where it was, which is why incomes and house prices are reported as medians — a handful of very large values would make the mean describe nobody. Quartiles here use the exclusive method: when the count is odd, the median itself is left out of both halves. That is Tukey's definition and what most courses teach. Spreadsheets disagree with each other on this, so a figure differing slightly from Excel is a convention difference rather than an error.
How the Median Calculator works
Paste any set of numbers for the median, mean, quartiles and interquartile range. The gap between the median and the mean is the useful output — it tells you whether a few extreme values are distorting the average.
Also known as: median and quartiles calculator · interquartile range calculator · q1 q3 calculator · how to find the median
Frequently asked questions
How do I find the median?
Sort the values and take the middle one. With an even count there is no single middle, so average the two either side of the centre.
When should I use the median instead of the mean?
Whenever a few extreme values would distort the average — incomes, house prices, response times. One billionaire moves the mean income of a town and leaves the median exactly where it was, which is why official statistics report medians.
How are the quartiles calculated?
By the exclusive method: with an odd count, the median itself is left out of both halves. That is Tukey's definition and what most courses teach. Spreadsheets disagree with each other here, so a small difference from Excel is a convention difference rather than an error.
What is the interquartile range for?
It measures spread using the middle half of the data, so it is unaffected by extremes in the way the standard deviation is not. It is also the basis of the usual outlier rule — anything beyond 1.5 × IQR from a quartile.
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