— Everyday Math
Average Calculator
Type, comma-separate or paste a list of numbers to get the mean, median, mode, range and count at once — with optional standard deviation, variance and the geometric and harmonic means, a running-sum table, and a chart of how the data is distributed.
Mean (average)
17
- Median
- 15
- Mode
- 15 (×2)
- Count
- 6
- Sum
- 102
- Minimum
- 8
- Maximum
- 30
- Range
- 22
— Values & running sum
| # | Value | Running sum |
|---|---|---|
| 1 | 8 | 8 |
| 2 | 12 | 20 |
| 3 | 15 | 35 |
| 4 | 15 | 50 |
| 5 | 22 | 72 |
| 6 | 30 | 102 |
— Distribution
Download— How it works
Mean = sum ÷ count (Σx ÷ n). Median = the middle value once sorted (the average of the two middle values if the count is even). Mode = the most frequently occurring value. Range = maximum − minimum.
Mean, median and mode — three kinds of “average”
The word “average” usually means the mean: add the numbers up and divide by how many there are. But it is only one of three common measures of the centre, and they can tell very different stories. The median is the middle value once the numbers are sorted — half the data lies above it, half below — and it is far less sensitive to a single extreme value. The mode is simply the value that occurs most often, which is the only one of the three that makes sense for things you cannot meaningfully add, like shoe sizes or survey choices.
When the data is roughly symmetric the three sit close together. When it is skewed — a few very large values, say — the mean is dragged toward the extreme while the median holds steady, which is exactly why incomes are usually reported as a median rather than a mean.
Worked example — the set 8, 12, 15, 15, 22, 30: Mean = (8 + 12 + 15 + 15 + 22 + 30) ÷ 6 = 102 ÷ 6 = 17. The median is 15 (the middle of the sorted list) and the mode is 15 (it appears twice) — so the mean is 17, but the typical value sits a little lower, pulled up by the 30.
Spread: range, variance and standard deviation
Two data sets can share the same mean yet look completely different — one tightly clustered, the other wildly scattered. The range (maximum − minimum) is the crudest measure of that spread. The standard deviation is the useful one: roughly, the typical distance of a value from the mean. The variance is just the standard deviation squared. Turn on “standard deviation & variance” under Advanced options to see both; this calculator reports the population figures (dividing by n), which describe the data you have entered rather than estimating a wider population.
Geometric and harmonic means — when the ordinary mean misleads
The ordinary (arithmetic) mean is the wrong tool for some jobs. For things that compound — investment returns, growth rates — use the geometric mean, the n-th root of the product of the values; averaging +50% and −50% arithmetically gives 0%, but you have actually lost money, and the geometric mean shows it. For averaging rates such as speed or price-per-unit, the harmonic mean is correct. Both require every value to be positive, and you will find them under Advanced options.
You can enter the numbers however suits you — typed with commas, separated by spaces, or pasted one per line from a spreadsheet — and the distribution chart shows how they cluster, while the table lists each value with a running total.
— Reader questions
What is the difference between mean, median and mode?
The mean is the sum divided by the count (the everyday “average”). The median is the middle value when the numbers are sorted. The mode is the value that appears most often. They coincide for symmetric data but diverge when the data is skewed — the mean is pulled toward extreme values, while the median is not.
When should I use the median instead of the mean?
Use the median when the data has outliers or is skewed, because a few very large or very small values distort the mean but barely move the median. Incomes, house prices and response times are usually summarised by the median for exactly this reason.
How do I enter or paste my numbers?
Type them separated by commas or spaces, or paste a whole column straight from a spreadsheet — one number per line works fine. The calculator splits on commas, spaces and new lines, and you can choose under Advanced options whether to ignore any non-numeric entries or count them as zero.
What does the standard deviation tell me?
It measures how spread out the numbers are — roughly the typical distance of a value from the mean. A small standard deviation means the values cluster tightly around the mean; a large one means they are widely scattered. This tool reports the population standard deviation (dividing by n).
What is the mode if every number is different?
If no value repeats, there is no mode, and the calculator says so. If two or more values tie for the most frequent, the data is multimodal and all of them are reported.
When is the geometric mean better than the ordinary mean?
For quantities that multiply rather than add — investment returns, growth rates and ratios. Averaging +50% and −50% arithmetically suggests no change, but you have actually lost 25%; the geometric mean captures that. It requires all values to be positive.