How to use it
Paste your values into the box. Separators do not matter — spaces, commas, semicolons, tabs and line breaks all work, so a column copied straight out of a spreadsheet pastes correctly without cleaning. Anything that does not parse as a number is skipped, and the count of skipped entries appears in the header strip. Always glance at that figure: a non-zero skip count usually means a stray label, a currency symbol or a thousands separator came along with the paste.
Results update as you type. The frequency table underneath lists every distinct value with its count, running cumulative total and percentage, with the modal value marked.
The three measures of centre
These three answer the same question — what is a typical value here? — and disagree in informative ways.
The mean adds every value and divides by how many there are. It uses all the information in the data, which is its strength, and it is the foundation of variance, standard deviation, regression and most inferential methods. Its weakness is that every observation gets a vote weighted by its magnitude, so a single extreme value shifts it. Add one billionaire to a room of a hundred people and the mean wealth becomes a number describing nobody present.
The median is the middle value once the data is sorted — or the average of the two middle values when n is even. It cares only about rank order, so an extreme observation can move arbitrarily far away without shifting it at all. That robustness is why income, house prices, response times and hospital stay lengths are almost always reported as medians.
The mode is the most frequently occurring value. It is the least used of the three for continuous data, where exact repeats may not occur at all, but it is the only one that works on categorical data. There is no mean shoe size preference or median favourite colour; there is a modal one. A distribution can also have no mode, or several.
Reading the gap between mean and median
The relationship between the mean and median is a fast diagnostic for the shape of a distribution, and this calculator reports it directly.
| Pattern | Shape | Typical cause |
|---|---|---|
| mean ≈ median | Symmetric | Heights, measurement error, test scores |
| mean > median | Right (positive) skew | A long tail of high values — income, wait times, sales per customer |
| mean < median | Left (negative) skew | A tail of low values — exam scores near a ceiling, age at death |
When the two diverge substantially, that divergence is a finding, not an inconvenience. Report both. A dataset where the mean is 42 and the median 28 is telling you something important about its tail that neither number conveys alone.
A worked example
Take the default data set: 12, 15, 15, 18, 22, 24, 24, 24, 27, 31, 33, 40 — twelve values.
- Sum = 12+15+15+18+22+24+24+24+27+31+33+40 = 285
- Mean = 285 ÷ 12 = 23.75
- Median: n is even, so average the 6th and 7th sorted values — (24 + 24) ÷ 2 = 24
- Mode: 24 appears three times, more than any other value — 24
- Range = 40 − 12 = 28
Mean 23.75 against median 24 is a difference of a quarter of a unit on data spread across 28 — near-perfect symmetry. The single value of 40 in the upper tail is not extreme enough to drag the mean meaningfully. Compare what happens if you change that 40 to 400: the median stays at 24, while the mean jumps to 53.75, a figure larger than every observation except one. That is the entire argument for the median in one edit.
Quartiles and the interquartile range
The calculator also reports Q1, Q3 and the IQR, because they describe spread in the same robust spirit as the median. Q1 is the value below which a quarter of the data falls; Q3 the value below which three quarters falls. The IQR is the distance between them — the width of the middle half of the data.
Outlier fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR
Those fences are the standard convention behind box plot whiskers. A point beyond them is conventionally flagged for inspection — not deleted. An outlier is a question, not a defect: it may be a transcription error, or it may be the most interesting observation in the set.
Which measure should you report?
- Roughly symmetric, no extreme values — the mean, and it will be close to the median anyway.
- Skewed or containing outliers — the median, ideally alongside the IQR rather than the standard deviation.
- Categorical or ordinal data — the mode, since neither of the others is defined.
- You need to do further statistics — the mean, because variance, standard deviation, confidence intervals and regression are all built on it. The median is descriptively better but analytically harder to work with.
- When unsure — report both and let the reader see the gap. That is more honest than picking the one that suits your argument.
Frequently asked questions
Can a data set have more than one mode?
What if no value repeats?
Why is my median not one of my data values?
Does the order I paste values in matter?
How many values can I paste?
Should I use this for grouped or frequency data?
Is my data stored?
Next steps
Once you know the centre of your data, the natural next question is how spread out it is — that is the standard deviation calculator. With a mean and a standard deviation in hand you can then ask how unusual any single observation is using the z-score calculator, or how precise your estimate of the mean actually is with the confidence interval calculator.