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mean, median, mode, variance, standard deviation

Statistics calculator

Paste numbers separated by commas, spaces or new lines to get the centre, the spread and the quartiles in one pass.

Up to 10,000 numbers. Commas, spaces, semicolons and new lines all work.

Short answer: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the median is 4.5, the mode is 4, the range is 7 and the population standard deviation is 2. The sample standard deviation is 2.138 — different denominator, different answer.

What each number is for

Mean and median describe the centre; range, variance and standard deviation describe the spread. Quartiles split the sorted list into quarters, which survives outliers better than a standard deviation does. Quoting a mean without a spread is how two very different datasets end up looking identical.

Worked example

Marks 42, 55, 61, 61, 70, 88: count 6, sum 377, mean 62.83, median 61, mode 61, range 46. The sample standard deviation is about 16.6, so a mark of 88 is roughly 1.5 standard deviations above the mean.

Statistics questions

What is the difference between mean and median?

The mean adds every value and divides by the count; the median is the middle value once the list is sorted. A single outlier drags the mean far more than the median, which is why income and house prices are usually reported as medians.

When do I use the sample standard deviation?

When the numbers are a sample drawn from a larger population, which is the usual case in experiments and surveys. It divides by n − 1. Population standard deviation divides by n and applies when your list is the entire population. Both are shown, labelled, because choosing the wrong one is a common and silent error.

How is the mode defined when nothing repeats?

This calculator reports no mode in that case, rather than picking the most frequent value arbitrarily. If several values tie for the highest frequency, all of them are listed.

How are the quartiles computed?

With linear interpolation between the closest ranks of the sorted list (the same method spreadsheets use). For small lists the choice of method changes the answer slightly, so the page follows one convention consistently instead of switching.

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