The mean tells you where a set of numbers sits; the standard deviation tells you how spread out it is. Two classes can both average 60 in an exam while one has everybody near 60 and the other has half at 30 and half at 90. Same mean, very different classes - and the standard deviation is what separates them.

Using it in three steps

1. 1 Paste or type your numbers. Commas, spaces and line breaks all work as separators, so a column copied from a spreadsheet goes in as it is.
2. 2 Read the summary row for the shape of the data: count, sum, mean, median, mode, range and the two extremes.
3. 3 Then pick the right column: sample if your numbers are part of a bigger group, population if they are the whole group.

Sample or population: why it matters

A sample underestimates spread, because the numbers you happened to collect sit closer to their own mean than to the true one. Dividing by n − 1 instead of n corrects for exactly that. For ten values the sample variance is about eleven percent larger, and it is the figure almost every statistics course asks for.

When there is no mode

If every value appears exactly once, this tool says there is no mode rather than listing all of them. Calling every number the most frequent one drains the word of meaning. When several values do tie for the top count, all of them are shown - a set can genuinely have two or three modes.