Standard Deviation: How to Calculate It Step by Step
Calculate sample standard deviation in four steps with two worked examples.
The steps
- 1. Find the mean
- 2. Square each distance from the mean
- 3. Add and divide by n − 1 (sample)
- 4. Take the square root
Standard deviation measures the typical distance of values from the mean.
Example 1
Find the sample standard deviation of 2, 4, 6.
- Mean = 4
- Squared distances: 4, 0, 4, sum = 8
- Variance = 8 ÷ 2 = 4
- s = √4 = 2
s = 2
Example 2
Which has the larger spread: 5, 5, 5 or 1, 5, 9?
- 5, 5, 5 has every value at the mean, so s = 0
- 1, 5, 9 has values far from the mean 5
1, 5, 9 has the larger spread
Common mistake
Dividing by n for a sample
For a sample, divide by n − 1. For a whole population, divide by n.
Standard deviation is never negative, and it uses the same units as the data.
Want more Statistics practice?
The free Statistics study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.
Open the Statistics guide