Statistics · Quick Reference

Variance Cheat Sheet

Statistics · Lesson 5/11

In one line: variance measures how spread out a dataset is around its mean — a small variance means data points cluster tightly; a large variance means they're spread widely.

Key Ideas

1What Variance Measures. The average of the squared differences between each data point and the mean.

2Why Squaring. Squaring the differences makes them all positive (so they don't cancel out) and emphasizes larger deviations more heavily.

3Population Variance. Divides the sum of squared deviations by n, the total number of values in the population.

4Sample Variance. Divides the sum of squared deviations by (n-1) instead of n — this correction (Bessel's correction) gives a better estimate of the population variance from a sample.

5Units of Variance. Variance is expressed in squared units of the original data (e.g., dollars-squared), which is part of why standard deviation is often preferred for interpretation.

Worked Examples

Find the population variance of 2, 4, 6, 8.

Population variance = 5

Find the sample variance of the same dataset: 2, 4, 6, 8.

Sample variance ≈ 6.67

Explain why sample variance uses (n-1) instead of n.

Dividing by (n-1) corrects for the bias introduced by estimating the mean from the sample itself

Formulas

Population variance = [sum of (x - mean)^2] / n

Sample variance = [sum of (x - mean)^2] / (n-1)

Practice Yourself

Find the population variance of 1, 2, 3, 4, 5.

Find the sample variance of 1, 2, 3, 4, 5.

2.5

Find the population variance of 10, 10, 10, 10.