Standard Deviation Calculator

What is Standard Deviation?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data 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.

It is one of the most common ways to measure spread and is widely used in fields such as economics, science, and quality control.

Population vs. Sample

When calculating standard deviation, it's important to know whether you are working with the entire population or just a sample.

Population (σ): Used when the dataset includes every member of the group being studied. For example, the height of every person in a country.
Sample (s): Used when the dataset is only a subset of a larger group. For example, the height of 100 randomly selected people.

Our calculator computes both values automatically.

How is Variance Related?

Variance is the square of the standard deviation. It also describes the spread of the data, but its unit is the square of the original values. Standard deviation is often easier to interpret because it is in the same unit as the original data.

Formulas

Population Standard Deviation (σ)

σ = \frac{\sum ( x _{i} - μ ) ^{2}}{N}

Where:

$σ$ = population standard deviation
$x_{i}$ = each value
$μ$ = population mean
$N$ = size of the population

Sample Standard Deviation (s)

s = \frac{\sum ( x _{i} - x ˉ ) ^{2}}{n - 1}