Average Calculator

Mean, median, mode, range and standard deviation from a list you paste — because "average" means three different things and they rarely agree.

Which Average Should You Use?

Use the median for money. House prices, salaries and rents are always skewed by a few huge values, and the mean gets dragged up to a number nobody actually pays.
Use the mean when values cluster symmetrically — test scores, heights, daily temperatures.
Use the mode for things that aren't numbers in spirit: the most common shoe size, the most frequent delivery day.
Check the count. If this reads fewer values than you pasted, something in your list isn't a number.

"Average" Is Three Different Words

When someone says average they usually mean the arithmetic mean: add everything up and divide by how many there are. But median and mode are averages too, and statisticians call all three measures of central tendency. The median is the value sitting in the middle once you sort the list, and the mode is whichever value shows up most often. On a tidy, symmetric set of numbers all three land in roughly the same place and the distinction does not matter. On real-world data, which is almost never tidy, they can be far apart — and which one gets quoted is often a choice about what story the number should tell.

When the Mean Lies

Take five salaries: 32,000, 35,000, 38,000, 41,000 and 251,000. The mean is 79,400, and not one person in that room earns anything close to it. The median is 38,000, which describes the group honestly. One extreme value dragged the mean more than 40,000 upward because the mean gives every value equal pull regardless of how far out it sits. The median cannot be dragged: it only cares about position in the sorted list, so an outlier moves it by one place at most. This is why national statistics offices report median household income and median house prices, and why a mean quoted without a median is worth a second look.

Picking the Right One

Income, wealth, house prices, rents: use the median. These distributions have a long right tail and the mean always overstates the typical case.
Exam scores, heights, blood pressure: the mean is fine, because values cluster around the middle without extreme tails.
Waiting times and page-load times: report the median and a high percentile. The mean hides the slow tail that users actually notice.
Categories rather than quantities — shoe size, most-ordered dish: only the mode makes sense.
Rates and speeds averaged over the same distance need the harmonic mean, not this one. 30 km/h out and 60 back averages 40, not 45.
Growth rates over time need the geometric mean. Two years of +50% and −50% is not 0% — it is a 25% loss.

Standard Deviation, and the n−1

The standard deviation says how far values typically sit from the mean. Two sets can share a mean of 50 and be nothing alike.
Variance is the standard deviation squared. It is what the maths actually works with; the standard deviation exists so the number is back in the original units.
Sample standard deviation divides by n−1, not n. This is Bessel's correction: a sample almost always underestimates the spread of the population it came from.
Use the population formula only when your list really is everything — all 30 pupils in the class, not 30 drawn from a school of 900.
With small lists the difference is large: at n=5, dividing by 4 instead of 5 raises the result by about 12%.
In a roughly normal spread, about 68% of values fall within one standard deviation of the mean and 95% within two.

Worked Examples

The same idea, two very different answers

Five test scores

88 + 92 + 79 + 95 + 84 = 438
438 ÷ 5 = 87.6 — the mean
Sorted: 79, 84, 88, 92, 95 — the middle is 88

Mean 87.6, median 88 — they agree

Five salaries, one outlier

32,000 + 35,000 + 38,000 + 41,000 + 251,000 = 397,000
397,000 ÷ 5 = 79,400 — the mean
Sorted, the middle value is 38,000 — the median

Mean 79,400, median 38,000 — trust the median

Frequently Asked Questions

How do I calculate an average?

Add all the numbers together and divide by how many there are. Five values summing to 438 give a mean of 87.6. That is the arithmetic mean — the median and mode are averages too, and this calculator returns all three.

What is the difference between mean and median?

The mean is the total divided by the count; the median is the middle value once the list is sorted. On symmetric data they are close. On skewed data — salaries, house prices — the mean is pulled toward the extremes and the median stays with the typical case.

When should I use the median instead of the mean?

Whenever a few very large or very small values could distort the picture. Money is the standard case: one 251,000 salary among four in the thirties pushes the mean to 79,400, a figure nobody earns. This is why official statistics report median income and median house prices.

What if there is no mode?

If every value appears exactly once, the set has no mode and this calculator says so rather than inventing one. If several values tie for most frequent, the set is multimodal and all of them are listed.

Should I choose sample or population?

Population if your list is genuinely everything you care about — all 30 pupils in a class. Sample if it is a subset standing in for a bigger group. The sample formula divides by n−1, which slightly raises the standard deviation to correct for a sample's tendency to understate spread.

Why does my count look wrong?

The count shows how many numbers were actually read. Separators are commas, spaces, semicolons and line breaks, and decimals must use a dot — a comma is treated as a separator, so "3,5" reads as two values, three and five.