Education / Statistics
Standard Deviation Calculator: Sample, Population and Working Table
Paste numbers to calculate sample or population standard deviation, variance and mean. Follow every value in a deviation and squared-deviation working table.
Standard Deviation Calculator: Sample, Population and Working Table: Starts with the sample calculation for 2, 4, 4, 4, 5, 5, 7 and 9. The mean is 5 and the squared deviations sum to 32: population variance is 4, while sample variance is 32/7. Each value appears in the working table. For median, quartiles and outliers, use the [statistics calculator](/statistics-calculator). Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
Separate values with commas, spaces, semicolons or new lines. Write decimals with a dot.
- Add the values and divide by the count: 40 ÷ 8 = 5.
- Subtract the mean from each value, then square each deviation. Their squared sum is 32.
- Divide the squared sum by 7: variance = 4.57142857143.
- Take the square root of the variance: standard deviation = 2.1380899353.
| Value | Deviation from mean | Squared deviation |
|---|---|---|
| 2 | -3 | 9 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 5 | 0 | 0 |
| 5 | 0 | 0 |
| 7 | 2 | 4 |
| 9 | 4 | 16 |
Displayed values are rounded; calculations use the full stored precision.
Standard deviation and variance
NIST explains sample standard deviation and variance in its measures of scale guide (https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm). The sample denominator is n − 1.
Working example
The eight starting values are an original illustrative dataset, released into the public domain. Sum = 40, mean = 5 and squared deviations sum = 32. OpenStax explains measures of spread (https://openstax.org/books/introductory-statistics-2e/pages/2-7-measures-of-the-spread-of-the-data). The worked table follows those definitions.
How to use it
- Paste numbers separated by commas, spaces or new lines.
- Choose sample or population, and the decimal mark if needed.
- Read the working table, copy the summary or download the table as CSV.
Privacy & limitations
Your inputs and files are processed in your browser. Nothing is uploaded.
Related tools
Frequently asked questions
When should I use sample SD?
Use sample SD when the values are a sample from a larger population. It divides the squared-deviation sum by n − 1. Population SD divides by n and describes the whole group you entered.
Why is sample SD undefined for one value?
Its denominator is n − 1, which becomes zero. The population SD of one value is zero.
Can I paste decimal-comma numbers?
Yes. Enable the decimal-comma option and separate values with spaces, semicolons or new lines. With that option off, commas are separators.
Does the table round the calculation?
Displayed values are rounded to twelve significant digits. The underlying calculation keeps the full available numeric precision.
Free tool · runs in your browser · no account required