Mean, Median & Standard Deviation Calculator

How to use

1. Paste your numbers. Spaces, commas, semicolons, tabs and line breaks all work, so a column copied from a spreadsheet needs no cleaning up.
2. Read the mean, median, mode and range in the summary.
3. Switch the spread between sample and population depending on where your numbers came from.
4. Check the quartiles for outliers before you trust the mean.

Features

• Takes a list however you have it: a spreadsheet column, a comma-separated line, or numbers scattered across several lines.
• Decides once whether commas are decimal points or separators, so a list is never read as a mixture of the two.
• Reports sample and population spread separately instead of picking one and hoping it was the one you needed.
• Quartiles by linear interpolation, matching Excel's QUARTILE.INC and NumPy's default, so the numbers agree with the tool you will check them against.
• Flags outliers by Tukey's rule — more than one and a half interquartile ranges outside the middle half.

Frequently asked questions

Is 1,5 one number or two?

It depends on the list, so the tool decides once for the whole list rather than per number. If every comma sits between two digits and no number has more than one, commas are decimal points and 1,5 2,5 is two values. Otherwise commas separate, so 1,2,3 is three values. It tells you which reading it used, and a list is never interpreted as a mixture of both.

Should I use the sample or the population standard deviation?

Sample, in almost every case. Use population only when your numbers really are the entire group you care about — every employee in the company, every order last month. If they are a sample standing in for something larger, dividing by n − 1 corrects a bias that otherwise makes the spread look smaller than it is. Spreadsheets call the sample version STDEV or STDEV.S.

Why is the median different from the mean?

Because the mean can be dragged by a single extreme value and the median cannot. Nine salaries of 30,000 and one of 900,000 have a mean of 117,000 — a figure nobody earns — and a median of 30,000. When the two disagree sharply, look at the outliers before quoting the mean to anybody.

How are the quartiles calculated?

By linear interpolation between the nearest ranks, the method Excel's QUARTILE.INC and NumPy's default percentile both use. This matters because several defensible methods exist and they disagree on small lists — Tukey's hinges will give a slightly different Q1 for eight numbers. Using the most widely implemented method means these figures match the tool you are most likely to check them against.

Related tools