What is standard deviation?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. Specifically, it is defined as the square root of the variance. Variance, in turn, measures how much the values in a data set deviate from the mean (average) of that data set. Therefore, when the variance is calculated, taking its square root gives the standard deviation, which provides a more interpretable value in the same units as the original data.

The standard deviation indicates how spread out the values are; a low standard deviation means that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. This measure is essential in statistics as it helps in understanding the distribution of data points relative to the mean.