Averages · The robust centre
Median Calculator
The median is the middle value once your numbers are sorted — half the data below it, half above. It is the 50th percentile, and unlike the mean it barely flinches when an outlier or a long tail shows up, which is exactly why incomes, house prices and response times are reported as medians. Paste your numbers for the median with the working shown, plotted right next to the mean so you can see when the two part company.
Tip: the default set ends in a lone 40. Delete it and watch the mean drop toward the median — the median itself hardly moves.
Result
In plain English
“The average” usually means the mean — add everything up, divide by the count. The median asks a different question: line the numbers up in order and step to the one in the middle. When a dataset is symmetric the two agree, but the moment it has a long tail they separate, and the gap between them is one of the most useful things you can know about your data.
- median
- The middle value of the sorted data. With an odd count it is the single central number; with an even count it is the average of the two central numbers. Exactly half the values fall on each side.
- the 50th percentile
- Another name for the median — the cut-off with 50% of the data at or below it. It is also the second quartile (Q2), the middle line of a box plot.
- mean vs median
- The mean shares the total out equally and so is tugged toward extreme values; the median counts positions, not sizes, and ignores how far out the extremes are. Mean above median means a right (high) tail; mean below means a left (low) tail.
- breakdown point
- How much of the data can be corrupted before a statistic gives a nonsense answer. The median’s is 50% — the highest possible. The mean’s is 0%: a single bad value can send it anywhere.
- robust, but forgetful
- Resisting outliers is the median’s strength and its cost: by using only ranks it discards the magnitudes, so for clean, symmetric data the mean uses more information and is the sharper estimate.
Frequently asked
How do I find the median by hand?
Sort the numbers from smallest to largest, then find the middle. If you have an odd count of values, the median is the one in the centre — at position (n + 1) ∕ 2. If you have an even count, there are two middle values, and the median is their average. For example, the sorted set 3, 5, 8, 9 has middle values 5 and 8, so the median is (5 + 8) ∕ 2 = 6.5. This calculator does the sorting and positioning for you and shows each step.
When should I use the median instead of the mean?
Use the median whenever the data are skewed or contain outliers — incomes, house prices, waiting times, anything with a long tail. The mean is pulled toward the extremes (a handful of billionaires lifts the “average” wealth far above what almost anyone has), while the median stays anchored on the typical case. A good rule: if the mean and median differ noticeably, report the median, and treat a quoted “average” with suspicion until you know which one it is.
Can the median be a value that is not in the data?
Yes, whenever you have an even number of values. The median is then the average of the two central numbers, which need not appear in the set — the median of 2, 4, 6, 8 is 5, a value that is not present. With an odd count the median is always one of the actual data points. Either way it marks the same place: the boundary with half the data on each side.
Why does one extreme value barely change the median?
Because the median depends on the order of the values, not their sizes. Pushing the largest number from 40 to 4,000 does not change which value sits in the middle — it is still the same one, so the median is unmoved. The mean, by contrast, adds that 4,000 into the total and divides, so it leaps upward. This is the median’s 50% breakdown point in action: up to half the values could be replaced by arbitrarily large numbers before the median is forced to budge.