Mean and Standard Deviation Calculator
Calculate the sum, arithmetic mean, population and sample variance, standard deviation, coefficient of variation, minimum, maximum and range of 2 to 10 numbers.
Things to keep in mind:
- At least 2 values are needed; the sample variance is undefined for a single value.
- At most 10 values can be entered; use a spreadsheet for larger datasets.
- Population and sample standard deviations differ; choose by whether your data is the whole population or a sample.
- The coefficient of variation can mislead when the mean is near zero or the data has negative values.
Calculator
Result
Enter the values and press Calculate to see the result here.
About this tool
This tool computes the basic descriptive statistics for 2 to 10 numbers: sum, arithmetic mean, variance, standard deviation, coefficient of variation, minimum, maximum and range. Only the first "number of values" fields are used; the remaining fields do not affect the result.
Formulas (n = number of values, x̄ = mean)
- Mean: x̄ = Σx / n
- Population variance: σ² = Σ(x − x̄)² / n; standard deviation σ = √σ²
- Sample variance: s² = Σ(x − x̄)² / (n − 1); standard deviation s = √s²
- Coefficient of variation: CV = s / |x̄| × 100 (shown as 0 when the mean is 0)
- Range: maximum − minimum
- Results are rounded half-up to 4 decimals (2 decimals for CV).
Example: for 2, 4, 4, 4, 5, 5, 7, 9 the sum is 40, the mean 5 and the sum of squared deviations 32. Population variance is 32/8 = 4 with σ = 2; sample variance is 32/7 = 4.5714 with s = 2.1381. CV = 2.1381 / 5 × 100 = 42.76%. The minimum is 2, the maximum 9 and the range 7.
How to read the result: the mean marks the centre of the data and the standard deviation shows how far values typically lie from it; a small value means the data are close to the mean, a large one means they are spread out. Use the population standard deviation when the data are the whole population, and the sample one (divided by n − 1) when they are a sample from a larger population. The coefficient of variation compares the spread of data sets of different scale as a percentage. Suitable for grades, measurements, prices and sales figures.
How to use
- Enter the number of values (2-10).
- Type the values into x1, x2, …; only the first "number of values" fields are used.
- Click Calculate and review the mean, standard deviations and the other measures.
Notes
Results are rounded HALF_UP to 4 decimals (2 for CV). Fields after the chosen count never affect the mean, standard deviation, minimum or maximum, whatever they contain. CV uses the sample standard deviation and shows 0 when the mean is 0.
Frequently asked questions
It measures how far values typically lie from the mean and is the square root of the variance. Small means values cluster near the mean; large means they are spread out.
The population version divides the sum of squared deviations by n, the sample version by n − 1 (Bessel's correction) to estimate the population variance without bias. It comes out slightly larger.
It is the standard deviation as a percentage of the mean, used to compare the spread of datasets with different units or magnitudes.
No. Only the first "number of values" fields count; default zeros or anything typed afterwards never changes any result, including min and max.
Results are rounded to 4 decimals. Rounding intermediate steps by hand can cause small differences in the last digit.
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