How to calculate standard deviation
- Paste or type your numbers, separated by commas, spaces or new lines.
- Choose Sample if the data is a sample of a larger group, or Population if it is the whole group.
- The standard deviation and variance appear at the top. The step-by-step table shows each deviation from the mean and its square.
The formula, step by step
1. Find the mean: add the numbers and divide by how many there are (n). 2. Subtract the mean from each number and square the result. 3. Add up the squares. 4. Divide by n − 1 for a sample, or by n for a population: this is the variance. 5. Take the square root to get the standard deviation.
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared deviations add up to 32. The population standard deviation is √(32 ÷ 8) = 2; the sample standard deviation is √(32 ÷ 7) ≈ 2.138. Dividing by n − 1 (Bessel's correction) makes the sample estimate unbiased, because a sample usually varies less around its own mean than the population does.
Standard deviation is in the same units as your data. In a roughly normal distribution, about 68% of values fall within one standard deviation of the mean and 95% within two. Your data never leaves your browser.
FAQ
What is the difference between sample and population standard deviation?
Sample standard deviation divides by n − 1 and estimates the spread of a larger population; population standard deviation divides by n and describes a complete data set.
What does a large standard deviation mean?
The values are spread far from the mean. A small one means they cluster closely around it.
Which Excel function matches?
STDEV.S matches the sample result and STDEV.P the population result.