A-level · Data presentation

Measuring correlation (the PMCC)Exam-style questions

The product moment correlation coefficient r as a number between −1 and 1 measuring linear correlation — computing it from the summary statistics S_xy, S_xx, S_yy, interpreting it in context, and why coding leaves it unchanged.

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15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
For $8$ pairs of data: $\sum x = 48$ , $\sum y = 96$ , $\sum xy = 676$ , $\sum x^2 = 360$ , $\sum y^2 = 1304$ . Find $r$ to 3 d.p.
Level 3 · 4 marksTry it
2
For $10$ pairs of data: $\sum x = 50$ , $\sum y = 100$ , $\sum xy = 590$ , $\sum x^2 = 300$ , $\sum y^2 = 1200$ . Find $r$ to 3 d.p.
Level 3 · 4 marksTry it
3
The product moment correlation coefficient between daily temperature and ice-cream sales is found to be $r = 0.88$ . Interpret this value in context.
Level 3 · 2 marksTry it
4
A student codes the variable $x$ using $p = \dfrac{x - 50}{5}$ and finds the PMCC between $p$ and $y$ to be $0.74$ . State, with a reason, the PMCC between $x$ and $y$ .
Level 3 · 2 marksTry it
5
The table shows five pairs of data.

$\begin{array}{c|ccccc} x & 1 & 2 & 3 & 4 & 5 \\\\ \hline y & 2 & 3 & 5 & 4 & 6 \end{array}$

Calculate the product moment correlation coefficient, to 3 d.p.
Level 3 · 4 marksTry it

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