Average calculator
Separate the numbers with commas, spaces or new lines. Mean and median are both reported, because they disagree whenever the data is skewed.
Result
- Mean
- 11.1667
- Median
- 10.5000
- Range
- 3.00 to 21.00
- Sum
- 67.0000
- Count
- 6
Worked examples
Mean and median compared
Six values: 12, 7, 3, 21, 9, 15.
- sum = 67
- 67 ÷ 6 = 11.17
- sorted: 3, 7, 9, 12, 15, 21
- median = (9 + 12) ÷ 2 = 10.5
Mean 11.17, median 10.5.
Mean, median and mode are all averages
"Average" is not one thing. The mean adds everything and divides by the count. The median is the middle value once sorted. The mode is whichever value occurs most often. Each answers a slightly different question about a typical value.
When a distribution is roughly symmetric they land close together. When it is skewed they separate, and the gap between them is itself informative.
When the mean misleads
The mean is pulled by extreme values. Nine people earning $30,000 and one earning $1,000,000 have a mean income of $127,000 — a figure nobody in the room earns. The median of $30,000 describes the group far better.
This is why income, house prices and response times are usually reported as medians. Where you see a mean quoted for skewed data, it is worth asking what the median was.
Weighted averages
A plain mean treats every value as equally important. When they are not — course credits, portfolio holdings, survey strata — each value needs a weight, and you divide by the sum of the weights rather than the count.
Averaging percentages is the usual place this goes wrong. A 50% success rate over 10 attempts and a 90% rate over 1,000 do not average to 70%; the combined rate is much closer to 90%.
Formula
mean = sum ÷ count
When mean and median diverge
The gap between them measures skew. Where they are far apart, quoting the mean alone is misleading.
| Data | Mean | Median | What it tells you |
|---|---|---|---|
| 10, 10, 10, 10, 10 | 10 | 10 | No spread at all |
| 8, 9, 10, 11, 12 | 10 | 10 | Symmetric — either is fine |
| 1, 2, 3, 4, 90 | 20 | 3 | One outlier drags the mean far from typical |
| 30k ×9, 1M ×1 | 127k | 30k | Classic income skew |
| 1, 2, 3, 4 | 2.5 | 2.5 | Even count — median is the middle pair averaged |
Which average to use
| Situation | Use | Why |
|---|---|---|
| Symmetric data | Mean | Uses every value and is easy to work with further |
| Income, house prices | Median | Resistant to a small number of very large values |
| Response times | Median or a percentile | Long tails pull the mean upward |
| Categories, not numbers | Mode | Mean and median are meaningless for labels |
| Values of unequal weight | Weighted mean | Credits, holdings and sample sizes must count differently |
| Rates and ratios | Harmonic mean | Averaging speeds by the arithmetic mean overstates them |
Frequently asked questions
How do I calculate the mean?
Add all the values together and divide by how many there are. For 12, 7, 3, 21, 9 and 15: the sum is 67 and there are 6 values, so the mean is 11.17.
What is the difference between mean and median?
The mean is the total divided by the count. The median is the middle value when sorted. The median is less affected by outliers, which is why it is preferred for skewed data like income.
How do I find the median of an even number of values?
Sort them and take the mean of the two middle values. For 3, 7, 9, 12, 15, 21 the middle pair is 9 and 12, so the median is 10.5.
Can a set of numbers have more than one mode?
Yes. If two values tie for the most frequent, the set is bimodal. If no value repeats, there is no mode at all.
Should I use the mean or the median?
Use the median when the data is skewed or contains outliers, and the mean when it is roughly symmetric. Reporting both is often the most honest option.
How do I calculate a weighted average?
Multiply each value by its weight, add the results, then divide by the total of the weights — not by the number of values.
Can the mean be a value that does not appear in the data?
Yes, and usually it is. The mean of 1 and 2 is 1.5, which is in neither. This is why an “average of 2.4 children” is not absurd.
What is the difference between average and mean?
In everyday use they are treated as the same thing, but “average” can refer to the mean, median or mode. “Mean” is unambiguous.
How do outliers affect the mean and median?
A single extreme value can move the mean a long way while leaving the median almost unchanged. That resistance is the median’s main advantage.
Why can I not average two percentages directly?
Because they may rest on different sample sizes. 50% of 10 and 90% of 1,000 combine to about 89.6%, not 70%.