What This Calculator Does

Paste a list of numbers and select sample or population scope to calculate count, mean, squared deviations, variance and standard deviation. Expand the steps table to inspect the first 50 observations; all observations contribute to the final result, including repeats.

When to Use It

Use it to describe the spread of measurements in the same unit. Sample mode estimates population variance from a sample; population mode treats the supplied values as the complete population of interest. To standardize a value see z-score. The P-value tool has separate test assumptions.

Inputs Explained

Separate numbers with commas, spaces, semicolons or line breaks. Use dot decimals: 1,5 means two values, not 1.5. Negative numbers, zero and scientific notation such as 1e3 are accepted. Limit: 10000 values and 200000 characters. Every value must be finite with absolute magnitude at most 1e100. Unit suffixes, currency symbols, thousands grouping and missing-value labels are rejected.

How the Calculation Works

Mean=Σx/n. Squared deviations=Σ(x−mean)². Population variance=squared deviations/n. Sample variance=squared deviations/(n−1). Standard deviation is the square root of variance. Sample mode needs at least two values. A one-value population has zero variance and standard deviation.

Example

For 2, 4, 6: count=3, mean=4, deviations=−2, 0, 2, squared deviations=4, 0, 4, and total=8. Population variance=8/3≈2.66666667 and standard deviation≈1.63299316. Sample variance=8/2=4 and standard deviation=2. Try example selects sample mode; changing scope clears the result until recalculated.