Question 13 - A-Level Maths

OCR H240/02 — Question 13 5 marks

Exam Board	OCR
Module	H240/02 (Pure Mathematics and Statistics)
Marks	5
Paper	Download PDF ↗
Topic	Bivariate data
Type	Interpret census or real-world data
Difficulty	Moderate -0.5 This question requires matching scatter diagrams to regions using means and standard deviations, then interpreting outliers in context. While it involves multiple steps and real-world interpretation, the statistical concepts are straightforward (reading means/SDs from data, identifying spread and location), and the matching process is systematic rather than requiring deep insight. It's slightly easier than average due to being primarily descriptive rather than requiring calculation or proof.
Spec	2.02c Scatter diagrams and regression lines 2.02i Select/critique data presentation

13 The table and the four scatter diagrams below show data taken from the 2011 UK census for four regions. On the scatter diagrams the names have been replaced by letters.
The table shows, for each region, the mean and standard deviation of the proportion of workers in each Local Authority who travel to work by driving a car or van and the proportion of workers in each Local Authority who travel to work as a passenger in a car or van.
Each scatter diagram shows, for each of the Local Authorities in a particular region, the proportion of workers who travel to work by driving a car or van and the proportion of workers who travel to work as a passenger in a car or van.

	Driving a car or van		Passenger in a car or van
	Mean	Standard deviation	Mean	Standard deviation
London	0.257	0.133	0.017	0.008
South East	0.578	0.064	0.045	0.010
South West	0.580	0.084	0.049	0.007
Wales	0.644	0.045	0.068	0.015

Region A \includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-14_634_1116_1308_299} Region B \includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-14_636_1109_2049_301} \includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-15_737_1183_237_240} \includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-15_723_1169_1046_246}

Using the values given in the table, match each region to its corresponding scatter diagram, explaining your reasoning.
Steven claims that the outlier in the scatter diagram for Region C consists of a group of small islands. Explain whether or not the data given above support his claim.
One of the Local Authorities in Region B consists of a single large island. Explain whether or not you would expect this Local Authority to appear as an outlier in the scatter diagram for Region B.

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13 The table and the four scatter diagrams below show data taken from the 2011 UK census for four regions. On the scatter diagrams the names have been replaced by letters.\\
The table shows, for each region, the mean and standard deviation of the proportion of workers in each Local Authority who travel to work by driving a car or van and the proportion of workers in each Local Authority who travel to work as a passenger in a car or van.\\
Each scatter diagram shows, for each of the Local Authorities in a particular region, the proportion of workers who travel to work by driving a car or van and the proportion of workers who travel to work as a passenger in a car or van.

\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
 & \multicolumn{2}{|c|}{Driving a car or van} & \multicolumn{2}{|l|}{Passenger in a car or van} \\
\hline
 & Mean & Standard deviation & Mean & Standard deviation \\
\hline
London & 0.257 & 0.133 & 0.017 & 0.008 \\
\hline
South East & 0.578 & 0.064 & 0.045 & 0.010 \\
\hline
South West & 0.580 & 0.084 & 0.049 & 0.007 \\
\hline
Wales & 0.644 & 0.045 & 0.068 & 0.015 \\
\hline
\end{tabular}
\end{center}

Region A\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-14_634_1116_1308_299}

Region B\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-14_636_1109_2049_301}\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-15_737_1183_237_240}\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-15_723_1169_1046_246}
\begin{enumerate}[label=(\alph*)]
\item Using the values given in the table, match each region to its corresponding scatter diagram, explaining your reasoning.
\item Steven claims that the outlier in the scatter diagram for Region C consists of a group of small islands.

Explain whether or not the data given above support his claim.
\item One of the Local Authorities in Region B consists of a single large island.

Explain whether or not you would expect this Local Authority to appear as an outlier in the scatter diagram for Region B.
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02  Q13 [5]}}

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