| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of the PMCC formula using given summary statistics. Students need only substitute values into a standard formula (Sxy/√(Sxx·Syy)) with minimal calculation steps. It requires recall of the formula and careful arithmetic but no problem-solving or conceptual insight beyond interpreting the correlation value. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit |
| Answer | Marks |
|---|---|
| \(S_{bb} = 65.7396 - \frac{36.22^2}{20} = 0.14518\) | M1 |
| \(S_{yw} = 259853 - \frac{2275^2}{20} = 1071.75\) | M1 |
| \(S_{bw} = 4128.03 - \frac{36.22 \times 2275}{20} = 8.005\) | M1 |
| \(r = \frac{8.005}{\sqrt{0.14518 \times 1071.75}} = 0.6417\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(r\) is fairly strongly +ve, supporting hypothesis | B2 | (7) |
**(a)**
$S_{bb} = 65.7396 - \frac{36.22^2}{20} = 0.14518$ | M1 |
$S_{yw} = 259853 - \frac{2275^2}{20} = 1071.75$ | M1 |
$S_{bw} = 4128.03 - \frac{36.22 \times 2275}{20} = 8.005$ | M1 |
$r = \frac{8.005}{\sqrt{0.14518 \times 1071.75}} = 0.6417$ | M1 A1 |
**(b)**
$r$ is fairly strongly +ve, supporting hypothesis | B2 | (7)
---2. A tennis coach believes that taller players are generally capable of hitting faster serves. To investigate this hypothesis he collects data on the 20 adult male players he coaches.
The height, $h$, in metres and the speed of each player's fastest serve, $v$, in miles per hour were recorded and summarised as follows:
$$\Sigma h = 36.22 , \quad \Sigma v = 2275 , \quad \Sigma h ^ { 2 } = 65.7396 , \quad \Sigma v ^ { 2 } = 259853 , \quad \Sigma h v = 4128.03 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the product moment correlation coefficient for these data.
\item Comment on the coach's hypothesis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [7]}}