Average calculator: mean, median, mode
Paste any list of numbers to get the mean, median, mode, range, sum and count instantly, plus quartiles and a sorted view of your data.
- Runs in your browser
- Nothing you enter is sent
- Free, no account
8 numbers recognised
Mean (average)
10.125
sum ÷ count
Median
8
middle value
Mode
7
most frequent
Range
18
max − min
Sum
81
Count
8
Minimum
3
Maximum
21
First quartile (Q1)
7
Third quartile (Q3)
12.75
Interquartile range
5.75
Standard deviation
5.693041
sample, n − 1
Geometric mean
8.770386
for growth rates
Harmonic mean
7.472202
for averaged rates
Midrange
12
Mean absolute deviation
4.40625
Step-by-step working
Add every value together.
Σx = 3 + 7 + 7 + 7 + 9 + 12 + 15 + 21 = 81Divide the sum by how many values there are — that is the mean.
mean = 81 ÷ 8 = 10.125Sort the values from smallest to largest to find the median.
3, 7, 7, 7, 9, 12, 15, 21With 8 values the median is the average of positions 4 and 5.
median = 8Count how often each value appears — the most frequent is the mode.
mode = 7Subtract the smallest value from the largest for the range.
range = 21 − 3 = 18
Frequency table
| Value | Count | Share | Distance from mean |
|---|---|---|---|
| 7 | 3 | 37.5% | −3.125 |
| 3 | 1 | 12.5% | −7.125 |
| 9 | 1 | 12.5% | −1.125 |
| 12 | 1 | 12.5% | +1.875 |
| 15 | 1 | 12.5% | +4.875 |
| 21 | 1 | 12.5% | +10.875 |
How to use it
Paste or type your numbers into the box. Commas, spaces, tabs, semicolons, pipes and newlines all count as separators, so a column copied straight out of Excel, Google Sheets or a CSV file works without any cleanup. Anything that is not a number is listed rather than silently ignored, so a stray header row cannot quietly skew your result.
Every statistic updates as you type. Use the copy buttons to take the whole summary or the sorted list away with you.
Mean, median and mode — and when each one is right
| Measure | How it is found | Best used when |
|---|---|---|
| Mean | Sum ÷ count | The data is roughly symmetric with no extreme outliers |
| Median | Middle value of the sorted list | The data is skewed — incomes, house prices, response times |
| Mode | The most frequent value | The data is categorical or you care about the most common case |
| Midrange | (min + max) ÷ 2 | A rough centre when you only have the extremes |
The classic illustration: nine people earning 30,000 and one earning 500,000 have a mean income of 77,000 and a median of 30,000. The median describes the typical person far better, which is why official statistics almost always quote it for income and property prices.
Reading the other numbers
- Range — the distance from smallest to largest. Simple, but one outlier controls it entirely.
- Q1 and Q3 — the values a quarter and three-quarters of the way through the sorted data.
- Interquartile range — Q3 − Q1, the spread of the middle half. Much more robust than the range.
- Standard deviation — the typical distance of a value from the mean; shown here as the sample version.
- Mean absolute deviation — the average distance from the mean, without squaring. Easier to interpret, harder to do algebra with.
- Geometric mean — the right average for growth rates and ratios; only defined when every value is positive.
- Harmonic mean — the right average for rates such as speed over a fixed distance; only defined when no value is zero.
How the median handles even counts
With an odd number of values, the median is the single value in the middle position. With an even count there are two middle values and the median is their average — so the median of 3, 7, 9, 12 is (7 + 9) ÷ 2 = 8. The step list shows the sorted data and names the positions used, so the number can be checked by eye.
When there is no mode, and when there are several
If every value appears exactly once, the data set has no mode and this tool says so rather than returning a meaningless first value. If several values tie for the highest frequency, all of them are reported — a data set can be bimodal or multimodal, and that is often the most interesting thing about it.
Which average for which job
- Exam marks — the mean, unless a few zeros from absent students are dragging it down.
- Salaries and house prices — the median, always.
- Annual investment returns — the geometric mean; averaging +50% and −50% arithmetically suggests break-even, but you have actually lost 25%.
- Average speed over a route — the harmonic mean of the leg speeds when the distances are equal.
- Shoe sizes to stock — the mode. Nobody wants the average shoe.
Performance and privacy
The calculation is a single pass over your data plus one sort, so tens of thousands of values are handled instantly in the browser. The frequency table lists the 30 most common values to keep the page fast. Nothing is uploaded — the tool works with the network disconnected.
Questions
What separators can I paste?
Commas, spaces, tabs, semicolons, pipes and newlines all work, so a column copied straight out of a spreadsheet pastes cleanly. Tokens that are not numbers are listed rather than silently dropped.
What happens when there is no mode?
If every value appears exactly once there is no mode, and the tool says so instead of inventing one. When several values tie for the highest count, all of them are listed.
How is the median found for an even count?
The list is sorted and the two middle values are averaged. The tool shows the sorted list with the middle position highlighted so you can check it by eye.
Which mean does it report?
The arithmetic mean is the headline figure. Geometric and harmonic means are also shown when they are defined, which is useful for growth rates and averaged rates respectively.