Standard deviation is a statistical measure of the amount of variation or dispersion of a set of values. It tells you how spread out the data is in relation to the mean (also called the expected value) of the set. A low standard deviation indicates 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. Standard deviation is often abbreviated as SD and is represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
To calculate the standard deviation, you can use the following formula:
$$\sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}}$$
where $\sigma$ is the standard deviation, $x_i$ is the value of the $i$th data point, $\mu$ is the mean of the data set, and $N$ is the total number of data points.
A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation is often considered a more robust, accurate measurement than other measurements of deviation such as range, which only measure the most dispersed points without consideration for the points in between.
