| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.8 This is a straightforward computational question requiring calculation of Pearson's r using the standard formula with given bivariate data. While tedious with 12 data points, it involves only routine application of a memorized formula with no conceptual challenges or problem-solving. The interpretation in part (b) is also standard recall of what correlation coefficients mean. |
| Spec | 2.02c Scatter diagrams and regression lines5.08a Pearson correlation: calculate pmcc |
| \(\boldsymbol { x }\) | 152 | 166 | 154 | 159 | 179 | 167 | 155 | 168 | 174 | 182 | 161 | 163 |
| \(\boldsymbol { y }\) | 143 | 154 | 151 | 153 | 168 | 160 | 146 | 163 | 170 | 175 | 155 | 158 |
1 The table shows the heights, $x \mathrm {~cm}$, and the arm spans, $y \mathrm {~cm}$, of a random sample of 12 men aged between 21 years and 40 years.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
$\boldsymbol { x }$ & 152 & 166 & 154 & 159 & 179 & 167 & 155 & 168 & 174 & 182 & 161 & 163 \\
\hline
$\boldsymbol { y }$ & 143 & 154 & 151 & 153 & 168 & 160 & 146 & 163 & 170 & 175 & 155 & 158 \\
\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, in context, your value calculated in part (a).
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2016 Q1 [5]}}