EXAMPLE 4 Calculating correlation

We have data on two variables, x and y, for n individuals. For the fossil data in Example 3, x is femur length, y is humerus length, and we have data for n = 5 fossils.

Step 1. Find the mean and standard deviation for both x and y. For the fossil data, a calculator tells us that

Femur:
Humerus:

We use sx and sy to remind ourselves that there are two standard deviations, one for the values of x and the other for the values of y.

Step 2. Using the means and standard deviations from Step 1, find the standard scores for each x-value and for each y-value:

Value
of x 		Standard score
 Value
of y 		Standard score
38 41
56 63
59 70
64 72
74 84

Step 3. The correlation is the average of the products of these standard scores. As with the standard deviation, we “average” by dividing by n − 1, one fewer than the number of individuals: