Statistics Calculator

What you get from one list of numbers

Paste in anything you have measured: test scores, daily sales, delivery times, prices. The calculator gives you the usual summary in one pass. Mean, median and mode say where the middle of the data is. Largest, smallest and range say how far it stretches. Standard deviation and variance say how tightly the values cluster around the mean. The sorted list at the bottom makes it easy to spot a typo or an outlier you did not expect.

A worked example you can check by hand

The starting numbers are 10, 12, 23, 23, 16, 23, 21, 16. There are 8 of them and they add up to 144, so the mean is 144 ÷ 8 = 18. Sorted, they read 10, 12, 16, 16, 21, 23, 23, 23. With an even count, the median is the average of the two middle values: (16 + 21) ÷ 2 = 18.5. The value 23 appears three times, so it is the mode. The range is 23 − 10 = 13. If you hit the same results on paper, you know the tool is doing what you expect.

Two standard deviations: which one do you want?

You will see a population figure and a sample figure side by side, and they differ because of one small step. If your list is the whole group, for example every student in one class, use the population standard deviation. If your list is only a sample taken to learn about a bigger group, such as 30 customers out of thousands, use the sample standard deviation, which divides by n − 1 instead of n. When in doubt about real survey or lab data, it is almost always the sample version. The Standard Deviation Calculator goes further, with a margin-of-error table for the mean.

Mean, median or mode: which one tells the truth?

They can disagree, and when they do, the gap is a clue. If a few very large values pull the mean far above the median, the data is skewed, which is common for incomes, house prices and waiting times. In that case the median is usually the fairer picture of a typical value. The mode is the right answer when you care about the most common category or size, such as the shoe size to stock most of. If you only need those three plus the range, with a clear explanation of each, the Mean, Median, Mode Calculator is a lighter tool.

When the geometric mean is the right average

The geometric mean multiplies the values and takes the nth root, instead of adding and dividing. Use it for numbers that grow by percentages. Say an investment gains 10% one year and 20% the next. The growth factors are 1.10 and 1.20, and their geometric mean is the square root of 1.32, which is about 1.1489, so the true average gain is roughly 14.9% a year, not the 15% a simple average suggests. The geometric mean is only meaningful for positive values, so it cannot describe a set that contains a negative growth factor. For real investment accounts with deposits and withdrawals, the Average Return Calculator handles the timing for you.

What to do with these numbers next

If you want to know how unusual one value is compared with the rest, turn it into a z-score. If you need a range that likely contains the true average of the whole group, feed the mean, standard deviation and count into the Confidence Interval Calculator. If you are planning a survey and wonder how many people to ask, try the Sample Size Calculator. And if you are working out the odds of something happening rather than describing data you already have, use the Probability Calculator.

Common questions