| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 4 |
| 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 correlation coefficient formula r = S_xy/√(S_xx × S_yy), requiring only substitution and calculator work. Part (c) tests understanding that correlation is scale-invariant, which is basic conceptual knowledge. No problem-solving or insight needed beyond formula recall. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc5.08c Pearson: measure of straight-line fit |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}} = \frac{-808.917}{\sqrt{113573 \times 8.657}} = -0.81579...\) | M1, A1 (2 marks) | M1 for knowing formula and clear attempt to substitute correct values. Root required for method. Anything rounding to \(-0.82\) for A1. Correct answer with no working award 2/2. |
| Answer | Marks | Guidance |
|---|---|---|
| Houses are cheaper further away from the station (or equivalent) | B1 (1 mark) | Context based on negative correlation only required. Accept "Houses are more expensive closer to the station" or equivalent. Require 'house prices' or 'station' and a clear correct comparison. |
| Answer | Marks | Guidance |
|---|---|---|
| \(-0.816\) | B1 (1 mark) | Accept anything rounding to \(-0.82\), or 'the same'/'unchanged' or equivalent. Award B1 if value quoted same as answer to (a). |
## Question 1:
**Part (a):**
$r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}} = \frac{-808.917}{\sqrt{113573 \times 8.657}} = -0.81579...$ | M1, A1 (2 marks) | M1 for knowing formula and clear attempt to substitute correct values. Root required for method. Anything rounding to $-0.82$ for A1. Correct answer with no working award 2/2.
**Part (b):**
Houses are cheaper further away from the station (or equivalent) | B1 (1 mark) | Context based on negative correlation only required. Accept "Houses are more expensive closer to the station" or equivalent. Require 'house prices' or 'station' and a clear correct comparison.
**Part (c):**
$-0.816$ | B1 (1 mark) | Accept anything rounding to $-0.82$, or 'the same'/'unchanged' or equivalent. Award B1 if value quoted same as answer to (a).
---\begin{enumerate}
\item A young family were looking for a new 3 bedroom semi-detached house. A local survey recorded the price $x$, in $\pounds 1000$, and the distance $y$, in miles, from the station of such houses. The following summary statistics were provided
\end{enumerate}
$$S _ { x x } = 113573 , \quad S _ { y y } = 8.657 , \quad S _ { x y } = - 808.917$$
(a) Use these values to calculate the product moment correlation coefficient.\\
(b) Give an interpretation of your answer to part (a).
Another family asked for the distances to be measured in km rather than miles.\\
(c) State the value of the product moment correlation coefficient in this case.\\
\hfill \mbox{\textit{Edexcel S1 2007 Q1 [4]}}