What is the formula for calculating the standard deviation?

The standard deviation measures the amount of variation or dispersion in a set of values. To calculate it, one must first find the variance, which represents the average of the squared differences from the mean. The standard deviation is then derived by taking the square root of the variance.

Thus, its primary formula illustrates how standard deviation relates directly to variance. Mathematically, if the variance is denoted as σ² (for a population) or s² (for a sample), the standard deviation is represented as σ (population standard deviation) or s (sample standard deviation). This ensures that the units of standard deviation are the same as those of the original data points, making it easier to interpret in that context. Understanding that standard deviation serves as a measure of data spread relative to the mean is crucial in fields like business statistics, where assessing risk and variability in data is vital.