| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Draw scatter diagram from data |
| Difficulty | Easy -1.3 This is a routine S1 statistics question requiring standard calculations (PMCC formula application) and basic scatter diagram plotting. Part (d) requires visual interpretation but no complex reasoning. All techniques are standard textbook exercises with no novel problem-solving required. |
| Spec | 2.05f Pearson correlation coefficient5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit |
| Plaque | \(\boldsymbol { x }\) | \(\boldsymbol { y }\) |
| A | 232 | 109 |
| B | 235 | 112 |
| C | 236 | 114 |
| D | 234 | 118 |
| E | 230 | 117 |
| F | 230 | 113 |
| G | 246 | 121 |
| H | 240 | 125 |
| I | 244 | 128 |
| J | 241 | 122 |
| K | 246 | 126 |
| L | 245 | 123 |
3 [Figure 1, printed on the insert, is provided for use in this question.]\\
The table shows, for each of a sample of 12 handmade decorative ceramic plaques, the length, $x$ millimetres, and the width, $y$ millimetres.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Plaque & $\boldsymbol { x }$ & $\boldsymbol { y }$ \\
\hline
A & 232 & 109 \\
\hline
B & 235 & 112 \\
\hline
C & 236 & 114 \\
\hline
D & 234 & 118 \\
\hline
E & 230 & 117 \\
\hline
F & 230 & 113 \\
\hline
G & 246 & 121 \\
\hline
H & 240 & 125 \\
\hline
I & 244 & 128 \\
\hline
J & 241 & 122 \\
\hline
K & 246 & 126 \\
\hline
L & 245 & 123 \\
\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 this question.
\item On Figure 1, complete the scatter diagram for these data.
\item In fact, the 6 plaques $\mathrm { A } , \mathrm { B } , \ldots , \mathrm { F }$ are from a different source to the 6 plaques $\mathrm { G } , \mathrm { H } , \ldots , \mathrm { L }$. With reference to your scatter diagram, but without further calculations, estimate the value of the product moment correlation coefficient between $x$ and $y$ for each source of plaque.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q3 [10]}}