How is standard deviation calculated?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. It is calculated by taking the square root of the variance, where variance itself is derived from the mean of the squared deviations from the mean of the dataset.

To calculate standard deviation, follow these steps: first, determine the mean (average) of the data set. Then, for each data point, calculate the deviation from the mean (subtract the mean from each data point). Next, square each of these deviations to eliminate negative values and emphasize larger deviations. Finally, compute the mean of these squared deviations to find the variance, and take the square root of that value to arrive at the standard deviation.

This process provides insight into how spread out the values are in relation to the mean, which is key in many statistical analyses, especially in understanding the distribution of data in GIS applications.