Standard deviation

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. It indicates how much the individual data points differ from the mean (average) of the dataset. A low standard deviation means that the data points are close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

The formula for calculating the standard deviation (σ) of a sample is:

where:

For a sample, the formula is slightly adjusted to:

where:

Standard deviation is widely used in various fields such as finance, engineering, and social sciences to assess risk, quality control, and variability in data. It provides valuable insights into the consistency and reliability of processes, measurements, and predictions.