A teacher asked a random sample of 10 students to record the number of hours of television, $t$, they watched in the week before their mock exam - Edexcel - A-Level Maths Statistics - Question 1 - 2013 - Paper 1

The product moment correlation coefficient $r$ is calculated using the formula:

$r = \frac{n \sum gt - \sum g \sum t}{\sqrt{(n \sum g^2 - (\sum g)^2)(n \sum t^2 - (\sum t)^2)}}$

Substituting the known values we have:

• $n = 10$
• $\sum gt = 1550.2$
• $\sum g = 63.6$
• $\sum t = 258$
• $\sum g^2 = \frac{(S_g + \frac{(\sum g)^2}{n})}{n}$
• $\sum t^2 = 8702$

After performing the calculations, we arrive at:

$r = -0.714956$

Thus, the correlation coefficient to three significant figures is:

Answer: $r = -0.715$

The correlation between $v$ (hours of revision) and $g$ (grade) is expected to be positive. This is because as the number of hours spent revising increases, students are likely to perform better in their exams. Thus, there is a direct relationship where higher revision time corresponds to higher grades.