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Standard Deviation and Variance
11. Variance


Variance is another measure that is used to describe the dispersion of elements of a dataset. The variance of a set of n observations is the average squared deviation of the data points from their mean \overline{x}, so it is closely related to the standard deviation. In fact, it is just a square of the standard deviation:

VAR=SD^2, SD=\sqrt{VAR}

The interpretation of variance is similar to that of standard deviation. A small variance indicates that observations are clustered close to the mean, whereas a large variance indicates that the elements of a dataset are spread out over a wider range of values. As with standard deviation, there is population variance (often denoted VARP) and sample variance (often denoted VAR. In this course, we'll use the word variance to mean population variance.

For example, the variance of the set {-1, 0, 1, 2} is easy to calculate if we know the standard deviation (calculated in the previous part of the course). It is equal to \frac{5}{4}. Variance is often used instead of standard deviation, especially in theory. In practice, many years ago, variance was also easier to calculate because it doesn't need the square root. Now, in the era of computers, calculating square roots is no longer an issue.