Standard Deviation Calculator
Guide: Mean, Median, Mode and Standard Deviation: A Plain Guide
- Standard deviation (sample)
- 2.13809
- Standard deviation (population)
- 2
- Mean
- 5
- Variance (sample)
- 4.571429
- Variance (population)
- 4
- Standard error
- 0.755929
- Minimum
- 2
- Maximum
- 9
- Quartiles (Q1, Q3)
- 4, 6
- Median
- 4.5
- Range
- 7
- Count
- 8
Divides by n − 1
Divides by n
Working
Mean = 5. For each number, subtract the mean and square the result. Add them up (32), divide by 8 for the population or 7 for a sample, then take the square root.
| Number | Minus the mean | Squared |
|---|---|---|
| 2 | -3 | 9 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 5 | 0 | 0 |
| 5 | 0 | 0 |
| 7 | 2 | 4 |
| 9 | 4 | 16 |
Nothing you enter or choose here leaves your device. This tool runs in your browser.
How to use
- 1Type or paste your numbers, separated by commas, spaces or new lines.
- 2Read the sample and population standard deviation.
- 3Check the working table to see how it was calculated.
Frequently asked questions
What is the difference between sample and population?
Use population when your numbers are every value there is. Use sample when they are a part of a larger group. A sample divides by n - 1, which gives a slightly larger result.
What does standard deviation tell me?
How spread out the numbers are around the mean. A small value means they are close together, and a large value means they are widely spread.
How is it calculated?
Subtract the mean from each number, square the results, add them up, divide by n (or n - 1 for a sample) to get the variance, then take the square root.
Why does one number give no sample result?
A sample needs at least two numbers, because it divides by n - 1, which would be zero.
Is my data sent anywhere?
No. Everything is worked out in your browser and nothing is sent to us.
Read the guide
Learn how this works and how to get the most from it.
Money, health & time
Mean, Median, Mode and Standard Deviation: A Plain Guide
What each average tells you, when the median beats the mean, how standard deviation measures spread, and when to use sample or population.
1 min read
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