Statistics Calculator
Paste any list of numbers and get every standard summary statistic at once — with each formula labelled so there's no confusion between population and sample versions.
About this calculator
Paste your data, hit Calculate, and get the full standard toolkit — center, spread, extremes and shape — in one place. For a deeper explanation of any individual measure, use the dedicated calculator below.
Every summary statistic, measure by measure
Each measure below gets a plain-English definition, the exact formula (with every symbol spelled out), a small diagram of what it's actually measuring, and a worked example — all in one card.
Center — mean and median
The mean is the arithmetic average and is sensitive to outliers. The median is the middle of the sorted list and is not. Reporting both — and letting the gap between them tell you about skew — is the fastest way to describe a data set's center.
Geometric mean
The Nth root of the product of N positive values. Use it for growth rates, ratios and any values on very different scales — the geometric mean treats a 2× change in one factor the same as a 2× change in another, which the arithmetic mean cannot.
Population vs sample standard deviation
Both measure spread around the mean. Use population σ (divide by N) when your data is the whole population. Use sample s (divide by N−1, Bessel's correction) when your data is a subset used to estimate a bigger population — the correction stops it under-reporting variability.
Variance
Variance is standard deviation squared — the mean of the squared distances from the mean. It's the workhorse in proofs (ANOVA, error propagation) but lives in the squared units of your data, which is why standard deviation is what people report.
Common mistakes
- Using population SD on a sample. Understates variability and biases every downstream statistic. If your data is a subset of a larger group, use the sample formula.
- Confusing variance and standard deviation units. If heights are in cm, SD is in cm but variance is in cm². Never compare a variance directly to a raw data value.
- Averaging percentages or growth rates with the arithmetic mean. Use the geometric mean, or averages compound incorrectly.
- Reporting "the mode" when the data is multimodal. If two or more values tie for the top count, all of them are modes.
- Treating range as a robust spread measure. A single outlier can inflate the range enormously; standard deviation and IQR are more stable.
Features of this calculator
- Thirteen summary statistics in a single result table — count, sum, mean, median, mode, largest, smallest, range, geometric mean, population and sample standard deviation, population and sample variance
- Every formula labelled inline so you know whether N or N−1 was used — no more guessing which flavour of standard deviation you got
- Bar chart of your values with mean and median drawn as reference lines
- Multimodal-aware — reports every value tied for the top frequency
- Copy the full result set in one click; sorted data always shown for verification
Frequently asked questions
+When should I use population vs sample standard deviation?
Population (divide by N) if the data IS the entire group of interest. Sample (divide by N−1) if the data is a subset used to estimate a larger population. When in doubt, use the sample formula.
+Why is my variance so large compared to the standard deviation?
Variance = SD². It's on the squared scale of the data, which is why standard deviation is what people usually report.
+Can I compute the geometric mean of negative numbers?
No — it's only defined for strictly positive values. This calculator shows "n/a" when any value is zero or negative.
+How many numbers can I enter?
There's no hard cap. The bar chart stays readable up to a few dozen values; the numeric results are exact for any length.
+Does this handle repeated values correctly?
Yes — repeated values are counted every time. That's what drives the mode calculation and is the reason the mean/median can differ from what you'd get from de-duplicated data.