How is standard deviation related to variance?

The standard deviation is a measure of the amount of variation or dispersion in a set of values. It is computed as the square root of the variance, which itself is the average of the squared differences from the mean. Therefore, when you take the square root of variance, you are essentially converting a measure of dispersion (variance) back into the original unit of measurement, allowing for a more intuitive understanding of spread in the data.

This relationship is crucial in statistics because while variance provides a measure of dispersion, it is in squared units, making it less interpretable than standard deviation, which is expressed in the same units as the data. Understanding this connection is fundamental for analyzing variability in any dataset.