| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.5 This is a standard computational question requiring calculation of the product moment correlation coefficient using the formula with given bivariate data. While tedious with 10 data points, it's a routine textbook exercise testing recall of the PMCC formula and careful arithmetic—no conceptual insight or problem-solving required beyond following the standard algorithm. |
| Spec | 5.08a Pearson correlation: calculate pmcc |
| \(\boldsymbol { x }\) | 1196 | 1062 | 1335 | 1429 | 1012 | 1355 | 1145 | 1417 | 1275 | 1284 |
| \(\boldsymbol { y }\) | 123 | 88 | 150 | 158 | 69 | 120 | 94 | 143 | 107 | 128 |
1 The weight, $x \mathrm {~kg}$, and the engine power, $y \mathrm { bhp }$, of each car in a random sample of 10 hatchback cars are shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 1196 & 1062 & 1335 & 1429 & 1012 & 1355 & 1145 & 1417 & 1275 & 1284 \\
\hline
$\boldsymbol { y }$ & 123 & 88 & 150 & 158 & 69 & 120 & 94 & 143 & 107 & 128 \\
\hline
\end{tabular}
\end{center}
\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.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-03_2484_1709_223_153}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2010 Q1 [5]}}