How is standard deviation calculated?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. To calculate the standard deviation, you begin by determining the variance of the dataset, which involves finding the average of the squared deviations from the mean. The final step to obtain the standard deviation is taking the square root of the variance. This process is important because standard deviation provides a measure that is in the same units as the original data, allowing for easier interpretation.

In contrast, calculating the mean involves simply finding the average of the dataset, which does not provide any information about the dispersion of the values. Dividing the variance by the number of data points is not a correct method for calculating standard deviation; instead, variance itself is calculated by averaging the squared deviations from the mean (and dividing by the number of data points is part of that process, but not for standard deviation). Averaging the absolute deviations from the mean is related to a different measure called the mean absolute deviation, not the standard deviation.

Thus, selecting the correct process of finding the square root of the variance leads directly to the accurate calculation of standard deviation, making it the right choice.