General
Average Calculator
Works averages, where the mean and the median tell different stories.
Result
The mean is pulled by outliers and the median is not. When one very large job sits in a list of small ones, the median usually describes your typical value better.
Get a Free Business AuditHow the calculation works
The mean is the sum divided by the count; the median is the middle value when ordered; the mode is the most frequent. Each is an average and they diverge whenever the distribution is skewed, which is why the choice is a substantive one rather than a technicality.
What moves the number
- Whether the distribution is skewed.
- Outliers, which move the mean and not the median.
- Sample size.
- Whether the values should be weighted.
Where this one goes wrong
A single large outlier moves the mean substantially and barely moves the median, which is why the mean is the wrong average for income, house prices, job values or anything else with a long tail, and quoting a mean for such data overstates the typical case. Use the median for skewed data. Weighting is the other issue, since an average of averages without weighting by the underlying counts produces a figure that corresponds to nothing.
Before you quote
- Use the median where the data is skewed.
- Check for outliers before quoting a mean.
- Weight an average of averages by the underlying counts.
Questions
About this calculator
Should I use the mean or the median?
The median where the data is skewed, which includes income, house prices and job values. A single large outlier moves the mean substantially and barely moves the median, so the mean overstates the typical case in a long-tailed distribution.
Can I average averages?
Only with weighting by the underlying counts. Averaging two averages drawn from samples of very different sizes produces a figure corresponding to nothing, and it is a common error in combining results across periods or groups.
What does the mode tell me?
The most frequent value, which is useful for categorical data and for spotting clustering that the mean and median both hide. A distribution with two peaks has a misleading mean and median and a revealing mode.
The formula
mean = sum of values ÷ number of values
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How to use this calculator
- Your numbers. Separate with commas, spaces or new lines.
The result updates as you type, so you can try a figure, see what it does to mean (average), and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| Your numbers | 420, 385, 610, 295, 480, 520 |
What comes out
| Result | Value |
|---|---|
| Mean (average) main result | 451.6667 |
| Median (middle value) | 450 |
| How many values | 6 |
| Range (max − min) | 315 |
Across 6 values the mean is 451.6667 and the median is 450. They total 2,710, ranging from 295 to 610.
What each figure means
- Your numbers
- Separate with commas, spaces or new lines.
What the results tell you
| Result | What it is |
|---|---|
| Mean (average) | The headline result. A number. |
| Median (middle value) | A number. |
| How many values | A number. |
| Range (max − min) | A number. |
Keep going
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