Statistics Calculator
Paste your numbers and get the whole picture — mean, median, spread, quartiles, outliers and a histogram.
Centre
Spread
Five-number summary
Shape
Distribution
Box plot
Whiskers reach the furthest point within 1.5 × IQR of the box. Anything beyond is flagged as an outlier.
Frequency table
| Value | Count | Frequency | Cumulative |
|---|
How to use this calculator
Step by step
- Paste or type your numbers into the box. Any separator works — spaces, commas, tabs or one number per line — so a column copied straight out of a spreadsheet needs no cleaning up.
- Say whether the numbers are a sample or the whole population. This changes the standard deviation and variance, and nothing else.
- Pick a quartile method if it matters to you. Exclusive matches most statistics textbooks; inclusive matches what a spreadsheet’s QUARTILE function returns.
- Read the four panels: centre, spread, five-number summary and shape. The sentence under the shape panel translates skewness and kurtosis into plain English.
- Look at the histogram for the overall shape and the box plot for outliers. Any point beyond 1.5 × IQR from the box is listed underneath in red.
Good to know
- Use sample unless you genuinely measured every member of the group. Dividing by n − 1 instead of n corrects the bias that comes from estimating the mean from the same data.
- When the mean and median are far apart, the mean is being dragged by a tail. For skewed data — incomes are the classic case — the median describes a typical value far better.
- The coefficient of variation is the standard deviation as a percentage of the mean, which lets you compare the spread of quantities measured in different units.
- An outlier is a flag, not a verdict. Check whether it is a typo, a genuine extreme, or a sign the data is not from one population at all — then decide.
- Fewer bins in the histogram show the broad shape; more bins show detail and noise. Set the bin count to 0 to let Sturges’ rule pick.
- Standard error is the standard deviation divided by √n — it estimates how much the mean itself would wobble if you drew another sample of the same size.
The maths behind it
- Mean x̄ = Σx ÷ n The balance point of the data.
- Sample variance s² = Σ(x − x̄)² ÷ (n − 1) Population variance divides by n instead.
- Standard deviation s = √s² Back in the original units, which is why it is quoted more often than variance.
- Standard error SE = s ÷ √n The spread of the sample mean, not of the data.
- Skewness g₁ = (Σ(x − x̄)³ ÷ n) ÷ s³ Zero is symmetric; positive means a right tail.
- Excess kurtosis g₂ = (Σ(x − x̄)⁴ ÷ n) ÷ s⁴ − 3 Measured against the normal curve, which scores zero.
- Outlier fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR Tukey’s rule, the standard behind every box plot.
Why does my calculator give a different Q1?
Because there are several accepted definitions of a quartile and they disagree on small data sets. Switch the quartile method between exclusive and inclusive — one of them will match your textbook or spreadsheet. Both are shown as a deliberate choice here rather than a silent default.
Sample or population — which do I want?
Population only if your numbers are the entire group you care about: every student in one class, every item in one batch. If the data stands in for something larger, it is a sample. When in doubt, sample is the safer choice because it gives the slightly larger, more cautious standard deviation.
What counts as a big skew?
As a rough guide: below 0.5 in absolute value is near-symmetric, 0.5 to 1 is moderate, and above 1 is strongly skewed. The plain-English sentence under the shape panel applies exactly those thresholds.
How much data can it handle?
Tens of thousands of values without complaint — everything runs in your browser and the sort is the slowest part. The frequency table gets long with continuous data, so it scrolls inside its own panel.