How this instrument works
Before any serious analysis, you describe: where is the data centred, and how far does it wander? The mean and median answer the first question two different ways — the mean is the balance point, the median the middle value. When they disagree noticeably, your data is skewed, and that disagreement is itself a finding.
The standard deviation answers the second question, and it comes in two flavours this instrument reports separately: the population form (divide by n) when your numbers are the whole story, and the sample form (divide by n−1) when they are a sample standing in for something larger. Textbooks fight about this; your data does not — it just needs you to know which one you are quoting.
Everything runs in your browser as you type. The data never leaves the page — paste exam scores, revenue figures or lab measurements without them touching any server.
- Paste or type your numbers — commas, spaces or new lines all work as separators.
- Read the headline mean; median, deviations, quartiles and extremes line up beneath it.
- Check the working block for the substitution — Σx, n, and the squared-deviation sum are all shown.
Worked example — the eight quiz scores
The default data set {2, 4, 4, 4, 5, 5, 7, 9} is the classic teaching example. Sum is 40 over n = 8, so the mean is exactly 5. Sort the list and the middle two values are 4 and 5, so the median is 4.5 — a touch below the mean, because the 9 drags the balance point right.
The squared deviations sum to 32. Population σ = √(32 ⁄ 8) = exactly 2; sample s = √(32 ⁄ 7) ≈ 2.14. Same data, two honest answers — the difference is only about whether these eight scores are the whole class or a sample of a bigger one.
Questions
Sample or population standard deviation — which one do I quote?
Ask whether your numbers are everything (all 8 quiz scores that exist → population, σ) or a sample standing in for more (8 customers out of thousands → sample, s). The sample form divides by n−1 to correct the bias of estimating the mean from the same data. When in doubt, quote the sample form — it is the conservative choice.
Why do my quartiles differ from my textbook's?
There are at least nine published quartile conventions. This instrument uses linear interpolation between closest ranks — the same method as the standard spreadsheet PERCENTILE function — so Q1 of the default set is 4, not the 3.5 some textbook methods give. Neither is wrong; they are different definitions, and this sheet states which one it uses.
When is the median better than the mean?
Whenever a few extreme values would mislead. One billionaire moving into a small town rockets the mean income while the median barely moves. Skewed data — incomes, house prices, response times — is usually summarised more honestly by the median; symmetric data by either.
How much data does this handle?
Thousands of values comfortably — it is a single pass of arithmetic in your browser. The practical limit is pasting, not computing. It needs at least two values, since spread is meaningless for one.