Standard Deviation Calculator
Calculate standard deviation, variance, and other statistics for a dataset.
What Is the Standard Deviation Calculator?
The standard deviation calculator measures how spread out a set of numbers is from its average. A low standard deviation means values are clustered near the mean; a high standard deviation means they are spread out. It supports both population and sample calculations.
Formula
How to Use
Choose whether your data represents an entire population or a sample. Enter your numbers separated by commas, spaces, or newlines. Click Calculate to see the standard deviation, variance, mean, and count.
Example Calculation
For the data 2, 4, 4, 4, 5, 5, 7, 9 (population): Mean = 5, Variance = 4, Standard Deviation σ = 2.
Understanding Standard Deviation
Standard deviation is one of the most important measures in statistics. It quantifies the amount of variation or dispersion in a dataset, telling you how much individual data points differ from the average.
In finance, standard deviation measures investment risk — higher deviation means more volatile returns. In manufacturing, it monitors quality control — products should have low deviation from specifications. In science, it indicates experimental precision.
The distinction between population and sample standard deviation matters. If you have data for every member of a group, use population (σ). If you have a subset, use sample (s), which divides by n−1 instead of n to correct for bias. This correction, known as Bessel's correction, prevents systematic underestimation of the true population variance.
Frequently Asked Questions
When should I use population vs sample?
Use population standard deviation when your data includes every member of the group. Use sample when your data is a subset. Sample uses n−1 (Bessel correction) instead of n to provide an unbiased estimate.
What is variance?
Variance is the square of the standard deviation. It measures spread in squared units, while standard deviation returns to the original units by taking the square root.
What does a standard deviation of 0 mean?
A standard deviation of 0 means all values are identical — there is no spread at all.