| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Misinterpretation of data in graphs |
| Difficulty | Easy -1.2 This is a straightforward statistics question requiring basic understanding of sampling vs population, simple linear substitution (Y=2009 into given equation), and interpretation of interpolation vs extrapolation. The hardest part (d) requires contextual reasoning about whether a Camden model applies to Croydon, but this is still accessible critical thinking rather than complex mathematical reasoning. |
| Spec | 2.01a Population and sample: terminology2.02c Scatter diagrams and regression lines5.09a Dependent/independent variables5.09d Linear coding: effect on regression |
| Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | ||
| 21300 | 23200 | 24200 | 25900 | 26900 | \#N/A | 28400 | 29400 |
| Answer | Marks | Guidance |
|---|---|---|
| eg sample, since only some data used oe; eg sample, since data for 2009 not used oe | B1 (2.2a) | sample, since not all data used; ignore further reasoning unless contradictory |
| Answer | Marks |
|---|---|
| £27 085 or £27 100 or £27 000 | B1 (3.4) |
| Answer | Marks | Guidance |
|---|---|---|
| it's interpolation oe; eg because we use 2009 oe which is between 2008 and 2010 | B1 (2.2a) | do not allow: eg 27085 lies between 2008 and 2010; eg 27085 lies between the values for 2008 and 2010 |
| eg a straight line model appears to be justified; eg relationship seems to be linear; eg median income seems to be directly proportional to time; eg positive correlation [between median income and year] | B1 (2.2b) | do not allow: eg positive association; eg positive relationship |
| Answer | Marks | Guidance |
|---|---|---|
| not reasonable oe since eg (median taxable) income varies considerably across different regions of London; eg (median) income different in Croydon and Camden; eg (median) income lower in Croydon (than Camden); eg pattern of change in income over time different in Camden to Croydon | B1 (2.4) | LDS advantage |
## Question 9(a):
eg sample, since only some data used oe; eg sample, since data for 2009 not used oe | B1 (2.2a) | sample, since not all data used; ignore further reasoning unless contradictory
## Question 9(b):
£27 085 or £27 100 or £27 000 | B1 (3.4) |
## Question 9(c):
it's interpolation oe; eg because we use 2009 oe which is between 2008 and 2010 | B1 (2.2a) | do not allow: eg 27085 lies between 2008 and 2010; eg 27085 lies between the values for 2008 and 2010
eg a straight line model appears to be justified; eg relationship seems to be linear; eg median income seems to be directly proportional to time; eg positive correlation [between median income and year] | B1 (2.2b) | do not allow: eg positive association; eg positive relationship
## Question 9(d):
not reasonable oe since eg (median taxable) income varies considerably across different regions of London; eg (median) income different in Croydon and Camden; eg (median) income lower in Croydon (than Camden); eg pattern of change in income over time different in Camden to Croydon | B1 (2.4) | LDS advantage9 The pre-release material contains information concerning the median income of taxpayers in different areas of London. Some of the data for Camden is shown in the table below. The years quoted in this question refer to the end of the financial years used in the pre-release material. For example, the year 2004 in the table refers to the year 2003/04 in the pre-release material.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
Year & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 & 2011 \\
\hline
\begin{tabular}{ l }
Median \\
Income in $\pounds$ \\
\end{tabular} & 21300 & 23200 & 24200 & 25900 & 26900 & \#N/A & 28400 & 29400 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Explain whether these data are a sample or a population of Camden taxpayers.
A time series for the data is shown below.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Median income of taxpayers in Camden 2004-2011}
\includegraphics[alt={},max width=\textwidth]{11788aaf-98fb-4a78-8a40-a40743b1fe15-07_624_1469_950_242}
\end{center}
\end{figure}
The LINEST function on a spreadsheet is used to formulate the following model for the data:\\
$I = 1115 Y - 2212950$, where $I =$ median income of taxpayers in $\pounds$ and $Y =$ year.
\item Use this model to find an estimate of the median income of taxpayers in Camden in 2009.
\item Give two reasons why this estimate is likely to be close to the true value.
The median income of taxpayers in Croydon in 2009 is also not available.
\item Use your knowledge of the pre-release material to explain whether the model used in part (b) would give a reasonable estimate of the missing value for Croydon.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q9 [5]}}