Math & Statistics

What Is Standard Deviation?

Standard deviation measures how spread out the values in a data set are around their mean. A small standard deviation means values cluster close to the average; a large one means they are widely scattered. It is the square root of the variance and is expressed in the same units as the data.

Sample vs. Population

Population standard deviation divides the sum of squared deviations by n. Sample standard deviation divides by n − 1 (Bessel's correction) and is used when the data is a sample drawn from a larger group.

Example

For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2.

The 68-95-99.7 Rule

For data that follows a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three.

🧮 Calculate It Yourself

Put Standard Deviation into practice with these free calculators — no sign-up, nothing stored.

📉 Standard Deviation Calculator Sample and population standard deviation and variance, with a step table. Calculate → 📊 Average Calculator (Mean, Median, Mode) Get the mean, median, mode, range, and sum of any list of numbers. Calculate →

🔗 Related Terms

Variance Mean (Average) Median

More Math & Statistics Terms

📖 Browse all glossary terms or explore all free calculators.

Last updated: September 27, 2026. This definition is for general educational purposes only. It is not financial, investment, tax, legal, or medical advice, and it does not recommend any product or course of action. For decisions about your own situation, consult a qualified professional.