| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Interpret census or real-world data |
| Difficulty | Moderate -0.8 This question tests basic conceptual understanding of correlation in a real-world context. Part (i) requires straightforward reasoning about positive correlation (larger areas have more of both) and negative correlation (proportions are complementary). Part (ii) involves standard interpretation of outliers' effects on correlation, all requiring recall of textbook concepts rather than calculation or novel insight. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc5.08c Pearson: measure of straight-line fit |
| \(x\) | ||
| \(y\) | ||
| \(a\) | ||
| \(b\) |
| Answer | Marks | Guidance |
|---|---|---|
| Both the number of employees using public transport and the number of employees using private vehicles depend on the LA population. | E1 [1] | AO 2.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Negative | E1ind | AO 2.2b |
| If a large prop use public transport then a smaller prop drive (and vice versa) | E1ind [2] | AO 2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Decrease the size of \(r\) or Make \(r\) less negative | E1 [1] | AO 2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| Little effect (because the population of the LA is small compared with the whole population) | E1 [1] | AO 2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| - Type 2 answers: Any suggested reason why few drive e.g. Few garages; Parking expensive or similar in context | E1 [1] | AO 2.4 |
# Question 11:
## Part (i)(a):
Both the number of employees using public transport and the number of employees using private vehicles depend on the LA population. | E1 [1] | AO 2.1 | or similar, but must be in context; Ignore all else | NOT No. using pt is prop to no. using pv |
## Part (i)(b):
Negative | E1ind | AO 2.2b | Ignore "strong" or "slight" etc | NOT Inverse prop'n; NOT "as $a$ increases $b$ decreases" unless in context |
If a large prop use public transport then a smaller prop drive (and vice versa) | E1ind [2] | AO 2.4 | or similar in context |
## Part (ii)(a):
Decrease the size of $r$ or Make $r$ less negative | E1 [1] | AO 2.2b | Make (value of) $r$ increase; $r$ closer to 0; Ignore "eg greatly"; Ignore all else | NOT Make $r$ decrease; NOT Weaken the corr'n; NOT Make corr'n less |
## Part (ii)(b):
Little effect (because the population of the LA is small compared with the whole population) | E1 [1] | AO 2.2b | or No effect or similar; Ignore all else |
## Part (ii)(c):
Ignore all reference to public transport
- Type 1 answers: People don't travel far to work; Jobs are close; High proportion walk (or cycle)
- Type 2 answers: Any suggested reason why few drive e.g. Few garages; Parking expensive or similar in context | E1 [1] | AO 2.4 | NOT just Few drive |
---11 Christa used Pearson's product-moment correlation coefficient, $r$, to compare the use of public transport with the use of private vehicles for travel to work in the UK.\\
(i) Using the pre-release data set for all 348 UK Local Authorities, she considered the following four variables.
\begin{center}
\begin{tabular}{ | l | c | }
\hline
\begin{tabular}{ l }
Number of employees using \\
public transport \\
\end{tabular} & $x$ \\
\hline
\begin{tabular}{ l }
Number of employees using \\
private vehicles \\
\end{tabular} & $y$ \\
\hline
\begin{tabular}{ l }
Proportion of employees using \\
public transport \\
\end{tabular} & $a$ \\
\hline
\begin{tabular}{ l }
Proportion of employees using \\
private vehicles \\
\end{tabular} & $b$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Explain, in context, why you would expect strong, positive correlation between $x$ and $y$.
\item Explain, in context, what kind of correlation you would expect between $a$ and $b$.\\
(ii) Christa also considered the data for the 33 London boroughs alone and she generated the following scatter diagram.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{London}
\includegraphics[alt={},max width=\textwidth]{65d9d34c-8c78-45fe-b9f0-dab071ae56bb-07_467_707_1366_653}
\end{center}
\end{figure}
One London Borough is represented by an outlier in the diagram.\\
(a) Suggest what effect this outlier is likely to have on the value of $r$ for the 32 London Boroughs.\\
(b) Suggest what effect this outlier is likely to have on the value of $r$ for the whole country.
\item What can you deduce about the area of the London Borough represented by the outlier? Explain your answer.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q11 [6]}}