How to calculate statistics
- Paste or type your numbers. Commas, spaces, semicolons and new lines all work, so you can paste a column straight from a spreadsheet.
- Choose Sample if your numbers are a sample from a larger group (the usual case), or Population if they are the complete group.
- Read the mean, median and standard deviation at the top, the full table below, and open Step-by-step to see how the standard deviation was worked out.
What the numbers mean
The mean is the sum divided by the count. The median is the middle value when sorted, which is not affected by extreme values. The mode is the most frequent value. The standard deviation measures how spread out the numbers are around the mean: about 68% of normally distributed data lies within one standard deviation of the mean, and 95% within two.
Sample standard deviation divides the sum of squared deviations by n − 1 instead of n (Bessel's correction). This compensates for the fact that a sample tends to be less spread out than the population it came from. Spreadsheets use the same split: STDEV.S for samples and STDEV.P for populations.
Quartiles are calculated as the medians of the lower and upper halves (excluding the overall median when n is odd), the method used by TI calculators and most textbooks. Spreadsheet QUARTILE functions interpolate and can give slightly different values for small data sets. Outliers are values more than 1.5 IQR beyond the quartiles.
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Should I use sample or population standard deviation?
Use sample unless your data includes every member of the group you care about, such as the marks of every student in one class when you only care about that class.
Why is the median different from the mean?
The data is skewed. A few very large or small values pull the mean towards them, while the median stays in the middle.
What if there is no mode?
When every value appears once, there is no mode. When several values tie for most frequent, all of them are listed.