| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| 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 calculation of the product moment correlation coefficient from a small dataset (n=5) using the standard formula. Part (i) requires only routine application of the PMCC formula with simple arithmetic, while part (ii) tests basic understanding of sampling (small sample size). This is easier than average as it's purely procedural with no conceptual challenges or problem-solving required. |
| Spec | 5.08a Pearson correlation: calculate pmcc |
| Number of people in the household | 2 | 3 | 3 | 5 | 7 |
| Number of cars belonging to people in the household | 1 | 1 | 3 | 2 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = -20; y = 11; x^2 = 96; y^2 = 31; xy = -52\) | B1 | |
| \(S_{xx} = 16\) or \(3.2\) | B1 | |
| \(S_{xy} = 6.8\) or \(1.36\) | B1 | |
| \(S_{yy} = 8\) or \(1.6\) | M1 | dep \(-1 < r < 1\); ft their \(S\)'s (\(S_{xx}, S_{xy}, +\)ve) for M1 only |
| \(r = \frac{8}{\sqrt{(16)(6.8)}}\) or \(\frac{1.6}{\sqrt{(3.2 \times 1.36)}}\) | A1 | 5 marks |
| \(= 0.767\) (3 sfs) | ||
| ii) Small sample oe | B1f | 1 mark |
**i)**
$x = -20; y = 11; x^2 = 96; y^2 = 31; xy = -52$ | B1 |
$S_{xx} = 16$ or $3.2$ | B1 |
$S_{xy} = 6.8$ or $1.36$ | B1 |
$S_{yy} = 8$ or $1.6$ | M1 | dep $-1 < r < 1$; ft their $S$'s ($S_{xx}, S_{xy}, +$ve) for M1 only
$r = \frac{8}{\sqrt{(16)(6.8)}}$ or $\frac{1.6}{\sqrt{(3.2 \times 1.36)}}$ | A1 | 5 marks
$= 0.767$ (3 sfs) | |
**ii)** Small sample oe | B1f | 1 mark
**Total for Question 2:** 6 marks2 The table contains data concerning five households selected at random from a certain town.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | }
\hline
Number of people in the household & 2 & 3 & 3 & 5 & 7 \\
\hline
Number of cars belonging to people in the household & 1 & 1 & 3 & 2 & 4 \\
\hline
\end{tabular}
\end{center}
(i) Calculate the product moment correlation coefficient, $r$, for the data in the table.\\
(ii) Give a reason why it would not be sensible to use your answer to draw a conclusion about all the households in the town.
\hfill \mbox{\textit{OCR S1 2007 Q2 [6]}}