Variance measures how spread out your data is. It is the average of the squared differences from the mean. Population variance divides by N, sample variance divides by (n − 1).

Should I use sample or population variance?

If your data is the entire population, use population variance (divide by N). If your data is a sample from a larger population, use sample variance (divide by n − 1).

Does this tool also give standard deviation?

Yes, it shows both variance and standard deviation for sample and population, plus mean, count, sum, min, max, and range.

Can I paste data from Excel?

Yes. Paste numbers separated by commas, spaces, semicolons, or new lines. The tool automatically detects and uses the numeric values.

Variance Calculator

Enter your data and get sample variance, population variance, their standard deviations, and descriptive statistics. This tool is meant to outperform one-purpose variance tools by giving you everything in one place.

Data set

Separate numbers with comma, space, semicolon or new line.

Calculation steps

For each data point xᵢ we show (xᵢ − mean) and (xᵢ − mean)². Sum of squares is used to get variance.

#	xᵢ	xᵢ − x̄	(xᵢ − x̄)²

Sum of squares:

Variance formulas

Population variance: \(\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2\)

Sample variance: \(s^2 = \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2\)

Standard deviation: \(\sigma = \sqrt{\sigma^2}, \; s = \sqrt{s^2}\)

FAQs

Why (n − 1) for sample variance?

Because we are estimating the population variance from a sample. Using n − 1 instead of n makes the estimator unbiased.

What if I only have one value?

Population variance will be 0 (no spread). Sample variance is undefined (division by 0) — we report “—”.

Why square the differences?

Squaring keeps all deviations positive and penalizes larger deviations more strongly.