Mean Practice

Now that we understand the basics of Sigma notation, let’s begin with some statistical formulas. The first one we’re going to look at is how to calculate the average of a set of data.

In statistics, we call the average the mean and it has this symbol: (bar{x}). When we put a bar over any variable, we are calculating the average of that data set.

Simply put, to calculate the average of a set of data, we add up (sum or (Sigma)) each of the data points and then we divide it by the total number of data points that we have. The number of data points is represented by the letter (n).

Here is the formula we use to calculate the mean:
(bar{x} = frac{Sigma (x)}{n})

If we applied this formula to our age scores (of which we have 4 data points), it would look like this:
(bar{x} = frac{Sigma (x)}{n})
(therefore bar{x} = frac{30 + 21 + 59 + 45}{4})
(therefore bar{x} = frac{155}{4})
(therefore bar{x} = 38.75)