Always look at a scatterplot first
Although the correlation coefficient is a good description of the strength of many relationships, it does not adequately describe others.
A scatterplot should always be examined to help assess whether there are features in the data that the correlation coefficient cannot describe.
Anscomb's data
The diagram below shows a scatterplot and several numerical summary statistics including the correlation coefficient.
The pop-up menu allows you to select one of four data sets. All four data sets have the same summary statistics, but the scatterplot shows that the relationships between X and Y are very different.
The important message is:
Don't just calculate summary statistics, look at a scatterplot of the data too.