Standard Deviation Calculator
Calculate the standard deviation and variance of a dataset. Displays results for both sample (s) and population (σ) formulas simultaneously.
Standard Deviation
5.2372
Variance (s²)
27.4286
Standard Deviation
4.899
Variance (σ²)
24
Count (N)
8
Mean (μ)
18
What is Standard Deviation?
In statistics, Standard Deviation is a measure of the amount of variation or dispersion of 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
When calculating standard deviation, you must choose between two distinct formulas based on the nature of your data:
- Population (σ): Use this formula when you have gathered data from every single member of the group you are studying. The formula divides the sum of squared differences by
N(the total number of values). - Sample (s): In scientific research, it is often impossible to measure an entire population, so you measure a random "sample". To correct for potential bias in a sample, Bessel's correction is applied. The formula divides the sum of squared differences by
N - 1. This makes the sample standard deviation slightly larger (and more conservative) than the population standard deviation.
Understanding Variance
Variance (σ² or s²) is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance. Variance is heavily used in finance and modern portfolio theory to measure the volatility of an asset.