How to describe the strength & direction of bivariate data correlation from a scatterplot (examples)

Scatterplots are a graphical way of representing bivariate (2-dimensional) data to see if a relationship (or association) exists between the variables involved. An example of bivariate data is arm span versus the height of person. We can observe that there is a strong association between the two variables. The taller a person, the greater their arm span in general. We will focus our discussion on bivariate data that shows a linear relationship (or none at all).

Non-linear relationships exist but are beyond the scope of what is covered. You will also notice that it may not be clear what you would categorise the strength of a relationship as. In fact, the upper end of moderate could overlap with the lower end of strong relationships. The correct answer would be one that you could plausibly justify by looking at the various points on the scatterplot and their distance from the central line.

The strength of the relationship can also be measured by calculating the correlation coefficient.