Average Calculator — Mean, Median and Mode

What this calculator does

Paste a list of numbers and this page works out the mean, median, mode, range, sum, and the population and sample standard deviation — all at once, with the working shown underneath the result. Everything runs in your browser: nothing you type is sent anywhere. The arithmetic is done in exact fractions rather than the usual floating-point numbers, so sums and averages that a spreadsheet would round come out exact — the mean of 0.1, 0.2 and 0.3 is shown as 0.2, not 0.20000000000000004. Only the square root used for the standard deviation is an approximation, and it is rounded to six decimal places.

Entering the numbers

Type or paste values into the box, separated by spaces, commas, semicolons or new lines — however you already have them, from a spreadsheet column or a line of text. Decimals and negative numbers are both fine. The calculator accepts up to 1,000 values, and each one can have at most 15 digits; anything longer or anything that isn't a number triggers an error message naming the value it could not read, so you can fix it without re-typing the whole list.

Mean, median and mode

The three “averages” answer different questions. The mean is the sum divided by the count: for 2, 4, 4, 4, 5, 5, 7, 9 the sum is 40 and there are 8 values, so the mean is 40 ÷ 8 = 5. The median is the middle of the sorted list. With an odd count it's the single middle value; with an even count, like these eight, it's the average of the two middle ones — here the 4th and 5th values are 4 and 5, so the median is (4 + 5) ÷ 2 = 4.5. The mode is the value that appears most often, which is 4 here (it appears three times). A list can have more than one mode if two or more values are tied for the most frequent; if every value is different, or every value repeats the same number of times, there is no mode, and the calculator says “None — no value repeats” rather than listing them all.

When the values are skewed, the three drift apart. A single salary of 1,000,000 in a list of ordinary salaries raises the mean a long way but barely moves the median, because the median only cares about which value sits in the middle, not how far the extreme values reach. That's why household income and house prices are usually reported as medians rather than means.

For school marks that need weights applied, a rounding rule, or the number of top marks still needed to hit a target, the grade average calculator is the better fit — this page treats every value equally unless you repeat a value to weight it yourself.

Range and standard deviation

The range is the largest value minus the smallest — for 2, 4, 4, 4, 5, 5, 7, 9 that's 9 − 2 = 7. The standard deviation measures how far values typically sit from the mean. To get it: take each value's distance from the mean, square that distance (so negative distances don't cancel positive ones), average the squared distances — that average is the variance — and take the square root of the variance to bring the units back to normal. For the list above, the squared distances add up to 32, the population variance is 32 ÷ 8 = 4, and the population standard deviation is √4 = 2 exactly.

There are two versions because there are two situations. Use the population figure (divide by the count, n) when your list is every value you care about — the marks of one whole class, say. Use the sample figure (divide by n − 1) when your list is a sample drawn from something larger, such as 20 people out of a much bigger population. For the same list, dividing by n − 1 = 7 gives a sample variance of 32 ÷ 7 ≈ 4.571 and a sample standard deviation of ≈ 2.138 — slightly larger than the population figure, because the smaller divisor corrects for a sample tending to sit a little closer to its own mean than to the true one. Spreadsheet programs label these STDEV.P and STDEV.S.

A second worked example: no mode, and a decimal list

Enter 10, 20, 30, 40 (one of the example chips above the form) and the mean is (10 + 20 + 30 + 40) ÷ 4 = 25, which also happens to be the median, since the two middle values, 20 and 30, average to 25. Every value here appears exactly once, so there is no mode. The range is 40 − 10 = 30.

Enter 1.5, 2.5, 3.5, 10 and the calculator handles the decimals the same way: sum 17.5, mean 4.375. Because the arithmetic is exact, a list like this never picks up the tiny rounding errors that binary floating point would add.

Reading the result

The mean is shown as the large primary figure, with the count and sum underneath. Below that, a summary table lists every statistic — count, sum, mean, median, mode, minimum, maximum, range, and both variances and standard deviations. A “How it was calculated” list spells out each step of the mean, median, variance and standard deviation with your own numbers filled in, and a “Values in order” line shows the full sorted list (the first 200 values, if you entered more). A copy button turns the summary table into plain text for pasting elsewhere, and a print button formats the page for printing.

Edge cases

• Empty input. Leaving the box blank and pressing Calculate shows “Enter at least one number.”
• One number. The mean, median, minimum and maximum all equal that number, and the range is 0. The sample variance and sample standard deviation need at least two values, so those two rows read “Needs at least 2 values.”
• A tie for the mode. If two or more values are equally the most frequent, all of them are listed as modes, with the shared count in brackets.
• Negative numbers. Treated normally throughout — a negative value can pull the mean down, and the range still works out correctly even when the smallest value is negative.
• Over 1,000 values, or a value over 15 digits. Both are rejected with a specific error message rather than silently truncated.

Common mistakes

The most common mix-up is treating the mean as if it always represents a “typical” value. In a skewed list — a handful of very high or very low numbers among many ordinary ones — the median is usually the more useful summary, since the mean gets pulled toward the extreme values. Another common error is picking the wrong standard deviation: using the sample figure (n − 1) on a full population slightly overstates the spread, and using the population figure (n) on a sample slightly understates it. When in doubt, ask whether your list is everything you care about (population) or a subset standing in for something bigger (sample).

Limitations

This calculator treats every entered value as equally important. If some values should count more than others — three tests worth different percentages of a grade, for instance — either repeat a value as many times as its whole-number weight, or use the grade average calculator, which takes weights directly. It also has no built-in way to remove outliers or exclude a value from just one statistic; edit the list itself if you want to compare “with” and “without” a particular number. For rounding a result to a specific number of decimal places, the rounding calculator can help, and for a simple percentage of marks the percentage calculator for marks is quicker than working it out by hand.

Frequently asked questions