Statistics Calculator
Paste a data set and get the count, sum, mean, median, mode, minimum, maximum, range, quartiles, interquartile range, variance and standard deviation. Choose whether your numbers are a sample or a whole population — it changes the variance and standard deviation, and this calculator is explicit about which it used.
Describe your data
How to use this calculator
- Paste or type your numbers. Commas, spaces and line breaks all work as separators, so a column copied from a spreadsheet can go straight in.
- Choose Sample or Population. If your numbers are everything you care about, that is a population; if they are a subset you are using to estimate something wider, that is a sample.
- Press Calculate for the count, sum, mean, median, mode, range, quartiles, variance and standard deviation.
Sample or population — why it changes the answer
The mean, median, mode and range do not care which you pick. Variance and standard deviation do.
A population variance divides the sum of squared deviations by n. A sample variance divides by n − 1 instead. The reason is that a sample's own mean sits closer to its own data than the true population mean does, so dividing by n would systematically underestimate the spread. Dividing by n − 1, known as Bessel's correction, removes that bias.
With large data sets the difference is small. With ten values or fewer it is not, which is exactly when people tend to get it wrong.
How the quartiles are calculated
Quartiles have several competing definitions and different tools disagree. This calculator uses the split-halves method, sometimes called Tukey's hinges: the median splits the data in two, and the median of each half gives Q1 and Q3, with the overall median excluded from both halves when the count is odd. It is the method taught in most school and undergraduate courses, and it is the one you get working by hand.
Spreadsheets do something different. Excel's QUARTILE.EXC and QUARTILE.INC interpolate between data points rather than taking the median of a half, so on the values 1 to 8 this calculator gives Q1 = 2.5 and Q3 = 6.5, QUARTILE.EXC gives 2.25 and 6.75, and QUARTILE.INC gives 2.75 and 6.25. None of them is wrong; they are different conventions. If your figures disagree with another tool by a small amount, this is almost always why.
Frequently Asked Questions
How do I calculate the mean, median and mode?
The mean is the sum divided by the count. The median is the middle value once the data is sorted, or the average of the two middle values when the count is even. The mode is the value that appears most often; this calculator lists every mode when several values tie, and reports no mode only when every value appears exactly once.
Should I choose sample or population?
Choose Population when your numbers are the whole group you care about, such as the marks of every pupil in one class. Choose Sample when they are a subset used to estimate something about a larger group. It changes only the variance and standard deviation, which divide by n and n minus 1 respectively.
What is the difference between variance and standard deviation?
Variance is the average squared distance from the mean. Standard deviation is its square root, which puts the figure back into the same units as the original data. That is why standard deviation is usually the one quoted.
Can I paste a column from a spreadsheet?
Yes. Values separated by commas, spaces or line breaks are all accepted, so a column copied straight out of a spreadsheet works without reformatting. Blank entries are ignored and anything that is not a number is reported rather than silently skipped.
Why do my quartiles differ from Excel or another calculator?
Because there is no single agreed definition. This calculator uses the split-halves method, where the overall median is left out of both halves before Q1 and Q3 are taken. Excel's QUARTILE.EXC and QUARTILE.INC interpolate between data points instead, so on the values 1 to 8 this calculator gives 2.5 and 6.5, QUARTILE.EXC gives 2.25 and 6.75, and QUARTILE.INC gives 2.75 and 6.25. None of them is wrong, they are different conventions.