Standard Deviation Calculator
Calculate standard deviation (σ and s) and variance for sample and population data sets. Enter your numbers to find the spread of your data instantly.
What is Standard Deviation?
Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Sample vs. Population Standard Deviation
- Sample ($s$): Used when your data represents a sample of a larger population. The formula divides by $N-1$ (Bessel's correction) to provide an unbiased estimator.
- Population ($\sigma$): Used when your data represents the entire population. The formula divides by $N$.
Formulas
Sample Standard Deviation:
s = √ [ Σ(x - x̄)² / (N - 1) ]
Population Standard Deviation:
σ = √ [ Σ(x - μ)² / N ]
? Frequently Asked Questions
Use Sample SD if your data is just a part of a larger group (e.g., surveying 100 people to represent a country). Use Population SD if you have data for every single member of the group you are interested in (e.g., the grades of everyone in your specific class).
Variance is simply the standard deviation squared. It measures the average degree to which each point differs from the mean. While standard deviation is in the same units as the data, variance is in squared units.
An SD of 0 means there is no spread in the data at all. Every single number in the dataset is exactly the same.