| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward application of the PMCC formula using given summary statistics. Students need only substitute values into a standard formula (no data processing required) and interpret the sign. The calculation is routine with no conceptual challenges beyond recalling the formula. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. they earn less from regular hrs so need more to supplement income | B1 | |
| \(S_{yy} = 420.58 - \frac{86^2}{18} = 9.69111\) | M1 | |
| \(S_{xx} = 830.25 - \frac{104.5^2}{18} = 223.569\) | M1 | |
| \(S_{xy} = 487.3 - \frac{86 \times 104.5}{18} = -11.9778\) | M1 | |
| \(r = \frac{-11.9778}{\sqrt{9.69111 \times 223.569}} = -0.2573\) | M1 A1 | |
| weak –ve correlation gives some support to hypothesis | B2 | (8) |
| e.g. they earn less from regular hrs so need more to supplement income | B1 | |
| $S_{yy} = 420.58 - \frac{86^2}{18} = 9.69111$ | M1 | |
| $S_{xx} = 830.25 - \frac{104.5^2}{18} = 223.569$ | M1 | |
| $S_{xy} = 487.3 - \frac{86 \times 104.5}{18} = -11.9778$ | M1 | |
| $r = \frac{-11.9778}{\sqrt{9.69111 \times 223.569}} = -0.2573$ | M1 A1 | |
| weak –ve correlation gives some support to hypothesis | B2 | (8) |2. A supermarket manager believes that those of her staff on lower rates of pay tend to work more hours of overtime.
\begin{enumerate}[label=(\alph*)]
\item Suggest why this might be the case.
To investigate her theory the manager recorded the number of hours of overtime, $h$, worked by each of the store's 18 full-time staff during one week. She also recorded each employee's hourly rate of pay, $\pounds p$, and summarised her results as follows:
$$\Sigma p = 86 , \quad \Sigma h = 104.5 , \quad \Sigma p ^ { 2 } = 420.58 , \quad \Sigma h ^ { 2 } = 830.25 , \quad \Sigma p h = 487.3$$
\item Calculate the product moment correlation coefficient for these data.
\item Comment on the manager's hypothesis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [8]}}