Standard Deviation Calculator
Calculate population and sample standard deviation, variance, and mean from a list of numbers.
Numbers (comma, space, or line separated)
Mean
5.5
8 values
Population σ
2.2913
σ² = 5.25Sample s
2.4495
s² = 6How to Calculate Standard Deviation
Standard deviation measures how spread out numbers are from the mean. It is calculated by: (1) finding the mean of all values, (2) computing each value's squared difference from the mean, (3) averaging those squared differences (the variance), and (4) taking the square root.
There are two versions: population standard deviation (divides by n, for the full dataset) and sample standard deviation (divides by n−1, when your data is a sample of a larger population). Enter comma-separated numbers below to see both.
Example
For 4, 8, 6, 5, 3, 7, 9, 2: the mean is 5.5. The squared differences are 2.25, 6.25, 0.25, 0.25, 6.25, 2.25, 12.25, 12.25. Population variance = 42/8 = 5.25, so population σ ≈ 2.2913. Sample variance = 42/7 = 6, so sample s ≈ 2.4495.
Common Use Cases
- Measuring the consistency or volatility of data (test scores, stock prices, measurements).
- Determining if a dataset has significant variability or is tightly clustered.
- Statistical analysis, quality control, and scientific research.
- Comparing the spread of two different datasets.
FAQs
When should I use population vs. sample standard deviation?
Use population standard deviation when your data represents the entire group you care about. Use sample standard deviation when your data is a subset of a larger population — the n−1 correction (Bessel's correction) compensates for the bias inherent in estimating from a sample.
What does a high or low standard deviation mean?
A low standard deviation means data points tend to be close to the mean (consistent). A high standard deviation means data points are spread out over a wider range (variable).
What units is standard deviation in?
Standard deviation is expressed in the same units as the original data. If your data is in meters, the standard deviation is also in meters.