Statistics · Quick Reference

Standard Deviation Cheat Sheet

Statistics · Lesson 6/11

In one line: standard deviation is the square root of variance — it measures spread in the same units as the original data, making it much easier to interpret directly.

Key Ideas

1Definition. Standard deviation = square root of variance. It tells you the 'typical' distance of data points from the mean.

2Population vs. Sample Standard Deviation. Population standard deviation (sigma) is the square root of population variance; sample standard deviation (s) is the square root of sample variance.

3Interpreting Standard Deviation. A small standard deviation means data points are close to the mean; a large one means they're spread out.

4Relationship to the Normal Distribution. In a normal distribution, about 68% of data falls within 1 standard deviation of the mean, and about 95% within 2 (the Empirical Rule).

5Comparing Datasets. Standard deviation lets you compare the consistency of two datasets even if they have the same mean — the one with the smaller standard deviation is more consistent.

Worked Examples

Find the population standard deviation of 2, 4, 6, 8 (population variance was found to be 5).

Approximately 2.24

Two classes have the same mean test score of 75. Class A has standard deviation 5, Class B has standard deviation 15. Which class has more consistent scores?

Class A has more consistent scores

If a dataset has standard deviation 0, what does that tell you?

All values in the dataset are exactly equal to the mean

Formulas

Standard deviation = square root of variance

Practice Yourself

Find the standard deviation of a dataset with variance 16.

Find the standard deviation of a dataset with variance 100.

If variance = 0, find the standard deviation.