# Variance Used to calculate how the data is spread around the population [[Mean]] Greek (mu). If calculating not estimating a population variance then the formula is: $population\ variance = \frac{\sum(x-\mu)^2}{n}$ we square the differences to ensure the value is positive and $n$ represents the population, to allow for skewing in a sample we do $n-1$ Once the variance has been calculated it is still squared so we need to take the square root of the entire things $population\ variance = \frac{\sum(x-\mu)^2}{n}$ If we were performing these calculations for a sample of a population (the most likely case) then the formula to use would look like this $sample\ variance = \frac{\sum(x-\bar x)^2}{n-1}$ the square root of the calculated result of the formula is the [[Standard Deviation]] of the sample values The variance is sensitive to outliers but it is a very useful value to have. ## Documentation <center> <iframe width="560" height="315" src="https://www.youtube.com/embed/SzZ6GpcfoQY" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> </center> ## Code ```r # This function uses n-1 by default for a population sample var(x, y = NULL, na.rm = FALSE, use) ```