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Variance calculator
The sample or population variance of your numbers as an exact fraction, with the working. Free, with no account or uploads.
Find the variance
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 variance
4.5714
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
- How is variance worked out?
- Take the mean from each number, square the differences, add them and divide by n − 1 for a sample or n for a population.
- Is the variance exact?
- Yes. It is worked out as an exact fraction; only the standard deviation, a square root, is rounded.
- What is the difference between variance and standard deviation?
- The standard deviation is the square root of the variance, in the same units as your numbers.
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