Question 13 - A-Level Maths

OCR H240/02 2021 November — Question 13 9 marks

Exam Board	OCR
Module	H240/02 (Pure Mathematics and Statistics)
Year	2021
Session	November
Marks	9
Paper	Download PDF ↗
Topic	Data representation
Type	Misinterpretation of data in graphs
Difficulty	Moderate -0.8 This question tests interpretation of pie charts and understanding of data representation rather than mathematical calculation. It requires reasoning about real-world contexts (rural vs urban, transport patterns) and understanding when different graph types are appropriate. While it involves multiple parts, each requires only straightforward logical reasoning without complex mathematical techniques—typical of accessible statistics questions at A-level.
Spec	2.02a Interpret single variable data: tables and diagrams 2.02i Select/critique data presentation

13 The four pie charts illustrate the numbers of employees using different methods of travel in four Local Authorities in 2011. \includegraphics[max width=\textwidth, alt={}, center]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-10_1131_1077_347_242}

\multirow[t]{4}{*}{Key:}	\multirow{4}{*}{\includegraphics[max width=\textwidth, alt={}]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-10_105_142_1578_465} }	Public transport
		Private motorised transport
		Bicycle
		All other methods of travel

State, with reasons, which of the four Local Authorities is most likely to be a rural area with many hills.
Explain why pie charts are more suitable for answering part (a) than bar charts showing the same data.
Two of the Local Authorities represent urban areas.
1. State with a reason which two Local Authorities are likely to be urban.
2. One urban Local Authority introduced a Park-and-Ride service in 2006. Users of this service drive to the edge of the urban area and then use buses to take them into the centre of the area. A student claims that a comparison of the corresponding pie charts for 2001 (not shown) and 2011 would enable them to identify which Local Authority this was. State with a reason whether you agree with the student.

Show mark scheme Show mark scheme source

Question 13:

Part (a)

Answer	Marks	Guidance
Answer	Mark	Guidance
A: High private and low public OR B: Low bicycle and low public OR B: Low bicycle and high private OR C: Low bicycle and high private	B2	Allow B1 for A or B or C with one correct factor only. Ignore else. All answers can be implied. Ignore all else.

Part (b)

Answer	Marks	Guidance
Answer	Mark	Guidance
Pie charts allow comparison of proportions. Pie charts show proportions. Ignore all else.	B1	NOT: Bar charts don't show proportions unless also state pies do. Assume "They" means pie charts. NOT: It's easier to compare data. Pie charts don't easily show which is greatest. Allow percentages instead of proportions.

Part (c)(i)

Answer	Marks	Guidance
Answer	Mark	Guidance
C and D	B1	Both, no others
Larger (or high or most) proportion public transport. Can be implied. Ignore all else.	B1	Dep applied to at least one of C and D, even if other LA mentioned. B-marks are independent.

Part (c)(ii)

Answer	Marks	Guidance
Answer	Mark	Guidance
LDS says method of travel is for longest part by distance. Method of travel is the type used for the longest part of the journey. Most people using Park-and-Ride would still say they were using private transport. People will still have to travel by car, so results won't be very different.	B1, B2	"Disagree" may be implied. Independent. Ignore all else.
(Alternatives assuming incorrectly users of P&R report both or just public): Public transport increase or private decrease	B1, B0	"Agree" may be implied. Ignore all else.
P&R will result in more people using private transport, so this will show an increase	B1, B0	Not just "Increase in private" without justification
Users of P&R will use both public and private, so not clear	B1, B0
No, because other changes might have been made that affect the proportions	B2
If P&R users report both, or just public, then yes, public will show increase	B2
Recognition of issue as to whether P&R users should report private or public. Hence unclear whether change will show	B1, B1	Other sensible answers may be seen not covered in this MS

# Question 13:

## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| A: High private and low public **OR** B: Low bicycle and low public **OR** B: Low bicycle and high private **OR** C: Low bicycle and high private | B2 | Allow B1 for A or B or C with one correct factor only. Ignore else. All answers can be implied. Ignore all else. |

## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Pie charts allow comparison of proportions. Pie charts show proportions. Ignore all else. | B1 | NOT: Bar charts don't show proportions unless also state pies do. Assume "They" means pie charts. NOT: It's easier to compare data. Pie charts don't easily show which is greatest. Allow percentages instead of proportions. |

## Part (c)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| C and D | B1 | Both, no others |
| Larger (or high or most) proportion public transport. Can be implied. Ignore all else. | B1 | Dep applied to at least one of C and D, even if other LA mentioned. B-marks are independent. |

## Part (c)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| LDS says method of travel is for longest part by distance. Method of travel is the type used for the longest part of the journey. Most people using Park-and-Ride would still say they were using private transport. People will still have to travel by car, so results won't be very different. | B1, B2 | "Disagree" may be implied. Independent. Ignore all else. |
| *(Alternatives assuming incorrectly users of P&R report both or just public):* Public transport increase or private decrease | B1, B0 | "Agree" may be implied. Ignore all else. |
| P&R will result in more people using private transport, so this will show an increase | B1, B0 | Not just "Increase in private" without justification |
| Users of P&R will use both public and private, so not clear | B1, B0 | |
| No, because other changes might have been made that affect the proportions | B2 | |
| If P&R users report both, or just public, then yes, public will show increase | B2 | |
| Recognition of issue as to whether P&R users should report private or public. Hence unclear whether change will show | B1, B1 | Other sensible answers may be seen not covered in this MS |

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Show LaTeX source

13 The four pie charts illustrate the numbers of employees using different methods of travel in four Local Authorities in 2011.\\
\includegraphics[max width=\textwidth, alt={}, center]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-10_1131_1077_347_242}

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
\multirow[t]{4}{*}{Key:} & \multirow{4}{*}{\includegraphics[max width=\textwidth, alt={}]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-10_105_142_1578_465}
} & Public transport \\
\hline
 &  & Private motorised transport \\
\hline
 &  & Bicycle \\
\hline
 &  & All other methods of travel \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item State, with reasons, which of the four Local Authorities is most likely to be a rural area with many hills.
\item Explain why pie charts are more suitable for answering part (a) than bar charts showing the same data.
\item Two of the Local Authorities represent urban areas.
\begin{enumerate}[label=(\roman*)]
\item State with a reason which two Local Authorities are likely to be urban.
\item One urban Local Authority introduced a Park-and-Ride service in 2006. Users of this service drive to the edge of the urban area and then use buses to take them into the centre of the area. A student claims that a comparison of the corresponding pie charts for 2001 (not shown) and 2011 would enable them to identify which Local Authority this was.

State with a reason whether you agree with the student.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2021 Q13 [9]}}

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