The Pearson correlation coefficient is a measure of the strength and direction of the linear relationship between two random variables. If we have a sample of data (xi,yi), i=1.,,,N, then the sample correlation is calculated according to the formula:
The correlation coefficient must lie between -1 and 1: -1 ≤ r ≤ 1.
The following image displays four datasets called Anscombe's quartet. In each case, the mean and standard deviation of each variable is the same, and the correlation between the two random variables is the same. However, the data look very different when graphed. The lesson: look at your data before you do your analysis.
This image is from the Wikipedia Commons.