Conceptual Difference Between Standard Deviation & Variance

Standard deviation and variance are two different ways that statisticians and scientists analyze how much data points are spaced out or squeezed together. More specifically, standard deviation and variance are used to measure how far individual data points are away from the mean of the data set. Understanding how spread out or squeezed in a data set is can help you infer other things about the data, like how strong a correlation is, how frequently a phenomenon is happening or if the data doesn’t point to any strong conclusions at all. Standard deviation and variance can also help you spot outliers. Outliers always tell a story. They also affect the results of every study where they show up.

The main relationship between variance and standard deviation is that they both use many of the same operations.

Variance is a calculation of how far numbers in a data set spread out from the average of that set. To find the variance of any given data set, first you have to find the data set’s mean. Find the mean by adding up all of the data points. Divide that sum by the number of data points in the set. The number you have now is the mean.

To get the variance, use the variance formula. Subtract the mean from each data point. Multiply each result by itself; in other words, find the square of each result. Now you have a new set of data points. Add these data points and then divide them by the number of data points you have, finding their mean or average. This average number is the variance.

To find the standard deviation of a data set, perform the above operations or use the variance formula to find the data set’s variance. After you have used the variance formula, take the square root of that number. Your new result is the standard deviation. Standard deviation is just the square root of a data set’s variance.

The relationship between variance and standard deviation lies primarily in their operations. Both are found using the mean of a data set. The variance measures how much on average each data point diverges from the mean. The larger the variances, the larger the range of their entire data sets.

The primary difference between variance and standard deviation is that variance emphasizes outliers more than standard deviation does.

Another difference between variance and standard deviation is that because of the squaring operation, the variance isn’t in the same measuring unit as its original data set anymore. Since finding the standard deviation of a data set requires doing the reverse – finding the square root – the standard deviation is in the same unit of measure as the original data points.