# Standard Deviation (Population)

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**Formula:**`σ = √(Σ(xi - μ)² / N)`

## Introduction to Standard Deviation Calculator

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. This formula represents the population standard deviation, which includes all members of a set.

## Parameter usage:

`...numbers`

= an array of numerical values

## Output:

`standard_deviation`

= the standard deviation of the input numbers

## Data validation

All inputs must be numerical values. If non-numerical values are entered or no values are provided, an error message will be displayed.

## Practical Application

Standard deviation is commonly used in finance, weather forecasting, and sports analytics to assess the variability of data.

Tags: Statistics, Standard Deviation, Variability, Population