Statistics Calculator

Mean, median, and mode

The arithmetic mean is the sum divided by the number of observations. The median is the middle ordered value, or the average of the two middle values when the count is even. The mode reports values that repeat most often; if every value occurs only once, this calculator reports no repeated mode.

Range, variance, and standard deviation

Range is maximum minus minimum. Variance measures average squared distance from the mean, and standard deviation is the square root of variance. This calculator uses a numerically stable one-pass variance algorithm to reduce avoidable rounding loss.

Population versus sample statistics

Population variance divides by N when your values are the full population of interest. Sample variance divides by N − 1 when the values are treated as a sample used to estimate a broader population. Sample variance and sample standard deviation are therefore undefined for a one-value dataset.

Geometric and harmonic means

The geometric mean is useful for multiplicative rates or proportional growth, while the harmonic mean is often useful for rates where equal quantities are involved. This tool reports both only when every input is strictly positive, avoiding ambiguous or non-real cases.

Interpreting descriptive statistics

These results describe the values you enter; they do not by themselves establish causation, statistical significance, representativeness, or a valid sampling design. Domain context still matters.

Frequently asked questions