Question 13 - A-Level Maths

OCR H240/02 2017 Specimen — Question 13 5 marks

Exam Board	OCR
Module	H240/02 (Pure Mathematics and Statistics)
Year	2017
Session	Specimen
Marks	5
Topic	Bivariate data
Type	Interpret census or real-world data
Difficulty	Moderate -0.8 This question tests interpretation of summary statistics (mean, SD) and scatter diagrams through pattern matching, requiring only basic understanding of how spread and central tendency appear visually. The reasoning is straightforward (matching numerical spreads to visual spreads) with no calculations needed, making it easier than average but not trivial due to the multi-part interpretation required.
Spec	2.02c Scatter diagrams and regression lines 2.02d Informal interpretation of correlation 2.02h Recognize outliers 2.02i Select/critique data presentation

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 On the scatter diagrams the names have been replaced by letters.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. \includegraphics{figure_13}

Using the values given in the table, match each region to its corresponding scatter diagram, explaining your reasoning. [3]
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. [1]
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. [1]

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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 On the scatter diagrams the names have been replaced by letters.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.

\includegraphics{figure_13}

\begin{enumerate}[label=(\alph*)]
\item Using the values given in the table, match each region to its corresponding scatter diagram, explaining your reasoning. [3]

\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. [1]

\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. [1]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2017 Q13 [5]}}

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