What is the difference between sample and population standard deviation?

Population standard deviation divides by n and describes a complete data set. Sample standard deviation divides by n − 1 and is used when your numbers are a sample drawn from a bigger group — the smaller divisor corrects the tendency of samples to understate spread. Statistics courses almost always want the sample version; both are shown here.

How is the median calculated for an even number of values?

The values are sorted and the two middle numbers are averaged. For 3, 7, 8, 12 the median is (7 + 8) ÷ 2 = 7.5.

What if no number repeats?

Then the set has no mode and the calculator says so. If several values tie for the highest count, all of them are listed — a set can be bimodal or multimodal.

Which quartile method does this use?

Linear interpolation between the closest ranks, the same method as Excel's QUARTILE.INC and Google Sheets' QUARTILE. Other textbooks use Tukey's hinges or the exclusive method, so a quartile may differ by a fraction from what your course expects.

Are my numbers sent to a server?

No. Everything is computed in JavaScript on your device. Nothing is uploaded or stored, and the page keeps working offline once loaded.

Statistics Calculator — Mean, Median, Mode & Std Dev

Your numbers

Decimals

Mean

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Median

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Mode

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Range

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Spread

Sample standard deviation (s): —
Population standard deviation (σ): —
Sample variance (s²): —
Population variance (σ²): —
Mean absolute deviation: —

Five-number summary

Count (n): —
Sum (Σx): —
Minimum: —
Maximum: —
Q1 · Q3 · IQR: — · — · —

Sorted values

Paste or type numbers above — commas, spaces, or one per line.

Paste a column from a spreadsheet or type numbers separated by commas, spaces, or line breaks. You get the mean, median, mode, range, quartiles, variance, and both sample and population standard deviation at once. Nothing is uploaded — the maths runs in your browser.

How it works

1
Paste your numbers Type or paste the data set into the box. Commas, spaces, tabs, and one-number-per-line all work, so a copied spreadsheet column needs no cleanup. Negatives and decimals are fine.
2
Read the summary Mean, median, mode, range, and standard deviation update as you type. Use the decimals dropdown to control rounding — set it to 4 when you need exam-grade precision.
3
Check the spread The quartile panel shows Q1, Q3, and the interquartile range, and flags any value outside the 1.5 × IQR fences as an outlier. Copy the whole summary with one click.

Your data stays private

All processing happens entirely in your browser. No files, text, or data are ever sent to our servers. You can disconnect from the internet and this tool will still work.

Frequently asked questions

What is the difference between sample and population standard deviation?: Population standard deviation divides by n and describes a complete data set. Sample standard deviation divides by n − 1 and is used when your numbers are a sample drawn from a bigger group — the smaller divisor corrects the tendency of samples to understate spread. Statistics courses almost always want the sample version; both are shown here.
How is the median calculated for an even number of values?: The values are sorted and the two middle numbers are averaged. For 3, 7, 8, 12 the median is (7 + 8) ÷ 2 = 7.5.
What if no number repeats?: Then the set has no mode and the calculator says so. If several values tie for the highest count, all of them are listed — a set can be bimodal or multimodal.
Which quartile method does this use?: Linear interpolation between the closest ranks, the same method as Excel's QUARTILE.INC and Google Sheets' QUARTILE. Other textbooks use Tukey's hinges or the exclusive method, so a quartile may differ by a fraction from what your course expects.
Are my numbers sent to a server?: No. Everything is computed in JavaScript on your device. Nothing is uploaded or stored, and the page keeps working offline once loaded.

From the blog

Mean, Median, Mode and Standard Deviation Explained What each summary statistic actually tells you, when the mean lies, and why n − 1 sits in the denominator. Read the post →