What is Standard Deviation?

Definition

What is Standard Deviation?

A Standard Deviation (or ) measures data dispersion in proportion to the mean. Data are grouped around the mean when it is low, while data are spread out when the deviation is high. We also refer to this type of deviation as volatility. This deviation is also considered a ‘risk.’ More precisely, it measures the average distance between the data values in the set and the mean.

Examples

$ \sigma = \sqrt{\frac{\sum (x_{i}-\mu)^{^{2}} }{N}} $

Where,
σ= population standard deviation
N= the size of the population
xi= the size of the population
μ= the population mean

Why is calculating it necessary?

This is a statistical tool that business leaders can use to assess and manage risk and make various decisions. This type of deviation is useful in business risk management applications to evaluate error margins in customer satisfaction surveys, stock price volatility, etc.