| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | March |
| Marks | 7 |
| Topic | Bivariate data |
| Type | Estimate correlation from scatter diagram |
| Difficulty | Easy -1.2 This is a straightforward interpretation question requiring visual assessment of a scatter diagram to identify positive correlation and select from given values. Parts (i)-(iii) test basic understanding of correlation concepts with no calculation, (iv) asks to identify an outlier visually, and (v) requires a contextual explanation. All parts are accessible recall and interpretation with no problem-solving or mathematical manipulation required. |
| Spec | 2.02d Informal interpretation of correlation2.05g Hypothesis test using Pearson's r |
| Answer | Marks | Guidance |
|---|---|---|
| Hence \(0.913\) is the correct value | B1, B1 | Dep on 1st B1 |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Sample is from one area, hence not random oe | E2 | Or might be different relationship elsewhere |
| [2] |
| Answer | Marks |
|---|---|
| Both depend on the size (of the pop) of area. | E1 |
| [1] |
| Answer | Marks |
|---|---|
| Correct point indicated (54200, 15300) | B1 |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| More local jobs (so higher proportion walk) | E1 | Any sensible equivalent, |
| [1] |
| Answer | Marks |
|---|---|
| Eg Fewer walk to work | E1 |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Eg Some businesses within the borough have closed down or have moved to the outskirts | E1 | or any relevant comment |
| [1] |
## 11(i)
Points close to straight line with +ve gradient
Hence $0.913$ is the correct value | B1, B1 | Dep on 1st B1
| [2]
## 11(ii)
Sample is from one area, hence not random oe | E2 | Or might be different relationship elsewhere
| [2]
## 11(iii)
Both depend on the size (of the pop) of area. | E1 |
| [1]
## 11(iv)
Correct point indicated (54200, 15300) | B1 |
| [1]
## 11(v)
More local jobs (so higher proportion walk) | E1 | Any sensible equivalent,
| [1]
## 11(vi)(a)
Eg Fewer walk to work | E1 |
| [1]
## 11(vi)(b)
Eg Some businesses within the borough have closed down or have moved to the outskirts | E1 | or any relevant comment
| [1]
---11 The scatter diagram shows data, taken from the pre-release data set, for several Local Authorities in one region of the UK in 2011. The diagram shows, for each Local Authority, the number of workers who drove to work, and the number of workers who walked to work.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{2011}
\includegraphics[alt={},max width=\textwidth]{6a6316e4-7b2d-4533-988a-4863d79ce668-08_483_956_479_557}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Four students calculated the value of Pearson's product-moment correlation coefficient for the data in the diagram. Their answers were $0.913,0.124 , - 0.913$ and - 0.124 . One of these values is correct. Without calculation state, with a reason, which is the correct value.
\item Sanjay makes the following statement.\\
"The diagram shows that, in any Local Authority, if there are a large number of people who drive to work there will be a large number who walk to work."
Give a reason why this statement is incorrect.
\item Rosie makes the following statement.\\
"The diagram must be wrong because it shows good positive correlation. If there are more people driving to work, there will be fewer people walking to work, so there would be negative correlation."
Explain briefly why Rosie's statement is incorrect.
\item The diagram shows a fairly close relationship between the two variables. One point on the diagram represents a Local Authority where this relationship is less strong than for the others. On the diagram in the Printed Answer Booklet, label this point A.
\item Given that the point A represents a metropolitan borough, suggest a reason why the relationship is less strong for this Local Authority than for the others in the region.
The scatter diagram below shows the corresponding data for the same region in 2001.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{2001}
\includegraphics[alt={},max width=\textwidth]{6a6316e4-7b2d-4533-988a-4863d79ce668-09_481_885_388_591}
\end{center}
\end{figure}
\item (a) State a change that has taken place in the metropolitan borough represented by the point A between 2001 and 2011.\\
(b) Suggest a possible reason for this change.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q11 [7]}}