| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.3 This is a standard S1 correlation calculation requiring systematic application of the PMCC formula with given data. While tedious with 8 data points, it involves only routine arithmetic and formula substitution with no conceptual challenges or problem-solving insight required. The interpretation parts are straightforward recall of correlation concepts. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit |
| \(\boldsymbol { x }\) | 223 | 276 | 374 | 433 | 564 | 612 | 704 | 766 |
| \(\boldsymbol { y }\) | 6.50 | 4.00 | 5.50 | 8.00 | 4.50 | 5.00 | 8.00 | 5.50 |
1 The table shows, for each of a random sample of 8 paperback fiction books, the number of pages, $x$, and the recommended retail price, $\pounds y$, to the nearest 10 p.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 223 & 276 & 374 & 433 & 564 & 612 & 704 & 766 \\
\hline
$\boldsymbol { y }$ & 6.50 & 4.00 & 5.50 & 8.00 & 4.50 & 5.00 & 8.00 & 5.50 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the value of the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value in the context of this question.
\item Suggest one other variable, in addition to the number of pages, which may affect the recommended retail price of a paperback fiction book.
\end{enumerate}\item The same 8 books were later included in a book sale. The value of the product moment correlation coefficient between the number of pages and the sale price was 0.959 , correct to three decimal places.
What can be concluded from this value?
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2006 Q1 [8]}}