Mean, median and standard deviation calculator
A list of numbers in, the statistics and the working out.
Examples temporarily replace the input and settings. You can restore your previous work.
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Output
Paste or type above to see the result here.
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Example
Example: population and sample standard deviation
Enter 2 4 4 4 5 5 7 9. The eight values sum to 40, so their mean is 5.
- The squared deviations from 5 sum to 32.
- For the population variance, divide by 8: 32 ÷ 8 = 4.
- For the sample variance, divide by 7: 32 ÷ 7 ≈ 4.571429.
| Measure | Result |
|---|---|
| Mean | 5 |
| Median | 4.5 |
| Mode | 4 |
| Population standard deviation | 2 |
| Sample standard deviation | ≈ 2.13809 |
Use the population result when these eight values are the whole group being described. The sample calculation uses n − 1 and gives a larger standard deviation.
How it works
- Type or paste the numbers, separated by spaces, commas or new lines — a column copied from a spreadsheet works.
- The mean, median and standard deviation appear first.
- Below them: the mode, range, quartiles, both variances with their formulas, and a table of each value’s deviation from the mean.
Frequently asked questions
- What is the difference between population and sample standard deviation?
- The population standard deviation σ divides the sum of the squared deviations by n; the sample one, s, divides by n − 1, because a sample tends to understate the spread. Use σ when you have every value, s when the numbers are a sample.
- How is the median found?
- Put the numbers in order and take the middle one; with an even count, the mean of the two middle ones: in 2, 4, 4, 4, 5, 5, 7, 9 it is (4 + 5) / 2 = 4.5.
- What if there are two modes?
- All of them are listed. If every value appears the same number of times, there is no mode.
- How are the quartiles worked out?
- As the medians of the lower and the upper half (the middle value left out when the count is odd), the method taught at school. Spreadsheets may use other methods and give slightly different quartiles.
- Is anything uploaded?
- No. It is worked out in your browser, and nothing you type leaves your computer.
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