Well done! You’ve calculated the variance of a data set. The full equation for the variance is as follows:

$\sigma^2 = \frac{\sum_{i=1}^{N}{(X_i -\mu)^2}}{N}$

Let’s dissect this equation a bit.

• Variance is usually represented by the symbol sigma squared.
• We start by taking every point in the dataset — from point number 1 to point number N — and finding the difference between that point and the mean.
• Next, we square each difference to make all differences positive.
• Finally, we average those squared differences by adding them together and dividing by N, the total number of points in the dataset.

All of this work can be done quickly using a function we provided. The variance() function takes a list of numbers as a parameter and returns the variance of that dataset.

dataset <- c(3, 5, -2, 49, 10)
var <- variance(dataset)