| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward application of the PMCC formula r = Sxy/√(Sxx·Syy) with all summary statistics provided. Requires only substitution and calculator work, no conceptual challenge or problem-solving—significantly easier than average A-level questions. |
| Spec | 5.08a Pearson correlation: calculate pmcc |
1 A production line in a rolling mill produces lengths of steel.\\
A random sample of 20 lengths of steel from the production line was selected. The minimum width, $x$ centimetres, and the minimum thickness, $y$ millimetres, of each selected length was recorded.
The following summarised information was then calculated from these records.
$$S _ { x x } = 2.030 \quad S _ { y y } = 1.498 \quad S _ { x y } = - 0.410$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value in the context of the question.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2012 Q1 [4]}}