What is Standard Deviation?

Definition

What is Standard Deviation?

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

Example of Standard Deviation

$ \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 standard deviation necessary?

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