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Standard deviation calculator
Sample or population standard deviation of your numbers, with every step on your own numbers. Free, with no account or uploads.
Find the standard deviation
Paste your numbers, then say whether they are a sample or the whole population.
These numbers are
A sampleThe whole population
A sample divides by n − 1, which corrects for seeing only part of the group.
Sample standard deviation
2.1381
Of 8 numbers: mean 5, median 4.5, mode 4.
- Count
- 8
- Sum
- 40
- Mean
- 5
- Median
- 4.5
- Mode
- 4 (3 times)
- Lowest and highest
- 2 and 9
- Range
- 7
- Quartiles (Q1, Q3)
- 4 and 5.5
- Interquartile range
- 1.5
- Variance
- 4.5714
- Standard deviation
- 2.13809
The working
- Mean = sum ÷ count = 40 ÷ 8 = 5.
- Take the mean from each number, square it and add: Σ(x − mean)² = 32.
- Divide by count − 1 = 7: variance = 4.5714.
- Standard deviation = √variance = 2.13809.
- Quartiles by straight lines between the sorted numbers at (n − 1) × ¼ and × ¾, as Excel's QUARTILE.INC and NumPy do; other methods give other quartiles.
Lead with
Standard deviationMeanVariance
Sums and means are exact; worked out in your browser, and nothing you type is sent anywhere or kept.
A little help along the way
Follow these steps. Every option is explained underneath. Everything runs in your browser; nothing is sent anywhere or kept.
- Say what you want to knowDescribe your numbers, a z-score, or a z-table.
- Paste or type your numbersSeparated by commas, spaces or new lines, and say whether they are a sample or a whole population.
- Read the answerThe figure you came for first, then every measure, and the working under it.
Questions people ask
- Sample or population standard deviation?
- Use sample when your numbers are part of a bigger group, which divides by n − 1; use population when they are the whole group, which divides by n.
- Does it show the working?
- Yes. Under The working: the mean, the squared differences added up, the division and the square root, on your own numbers.
- How do I enter my numbers?
- Paste or type them separated by commas, spaces or new lines.
This page is the Statistics calculator, opened for this one job; every other tool it has is one press away. Each of its settings is explained on the Statistics calculator's own page.
Read the step-by-step guide