Five made-up students sit two short tests…

Step 1. Deviations. Test A: $-2, 1, -5, 4, 2$. Test B: $-1, 2, -5, 0, 4$.

Step 2. The sums. $S_{AA} = 4 + 1 + 25 + 16 + 4 = 50$. $S_{BB} = 1 + 4 + 25 + 0 + 16 = 46$. $S_{AB} = 2 + 2 + 25 + 0 + 8 = 37$.

Step 3. The standard deviations. $s_A = \sqrt{\dfrac{50}{4}} = 3.5355$ marks and $s_B = \sqrt{\dfrac{46}{4}} = 3.3912$ marks.

Step 4. r. $r = \dfrac{37}{\sqrt{50 \times 46}} = 0.7715$. The z-score route gives the same: $\dfrac{37}{4 \times 3.5355 \times 3.3912} = 0.7715$.

What it means. A moderate to strong positive pattern: students who do well in one test tend to do well in the other, with exceptions such as the fourth student.