| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Assess appropriateness of correlation analysis |
| Difficulty | Moderate -0.8 This is a straightforward data handling question requiring basic understanding of sampling methods, missing data, and outlier identification. Parts (a) and (b) test simple conceptual knowledge (recognizing non-random sampling and missing values), while part (c) requires visual identification of outliers from a scatter diagram—all routine AS-level statistics tasks with no calculation or complex reasoning required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.02j Clean data: missing data, errors |
| Area | Median Income of Taxpayers | Percentage of Pupils Achieving at Least 5 A*- C grades including English and Maths |
| City of London | 61100 | \#N/A |
| Barking and Dagenham | 21800 | 54.0 |
| Barnet | 27100 | 70.1 |
| Bexley | 24400 | 55.0 |
| Brent | 22700 | 60.0 |
| Bromley | 28100 | 68.0 |
| Camden | 33100 | 56.4 |
| Croydon | 25100 | 59.6 |
| Ealing | 24600 | 62.1 |
| Enfield | 25300 | 54.5 |
| Greenwich | 24600 | 57.7 |
| Hackney | 26000 | 60.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Not a simple random sample, since not all sets of 12 possible samples have an equal chance of being chosen in this way | B1 | Or equivalent; Not random as first 12 areas chosen; Convenience |
| Answer | Marks | Guidance |
|---|---|---|
| \#N/A means there was no data available | B1 | No data so no relationship can be established |
| and we cannot use median income on its own | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| the 3 largest \(x\)-values ringed | B1 | No extra points ringed |
| Answer | Marks | Guidance |
|---|---|---|
| \(60.9(074)\) obtained, which is close to \(60.4\) so a good fit | B1 | Must be some evidence of comparison |
| Answer | Marks | Guidance |
|---|---|---|
| \(92.669 - 92.7\) | B1 | awrt 92.7 |
| Answer | Marks | Guidance |
|---|---|---|
| extrapolation | B1 | Or equivalent; Causation with explanation |
| It would be an outlier. This model was calculated without outliers. | B1 | Might live in different boroughs than they go to school in; City of London's median would be an outlier compared to other areas; \(P=92.67\) with median £61100 with relevant comment; Not many schools in City of London |
| Answer | Marks | Guidance |
|---|---|---|
| from diagram, percentage is above 50% in all areas and data is for 5 or more passes including English and Maths, so there is evidence to support this statement | B1 | Not proves; All points on scatter graph are above 50% so suggests statement is correct; percentage is above 50% in all areas and data is for 5 or more passes including English and Maths, so there is evidence to support this statement |
## Question 11(a):
Not a simple random sample, since not all sets of 12 possible samples have an equal chance of being chosen in this way | B1 | Or equivalent; Not random as first 12 areas chosen; Convenience
---
## Question 11(b):
\#N/A means there was no data available | B1 | No data so no relationship can be established
and we cannot use median income on its own | B1 |
---
## Question 11(c):
the 3 largest $x$-values ringed | B1 | No extra points ringed
---
## Question 11(d):
$60.9(074)$ obtained, which is close to $60.4$ so a good fit | B1 | Must be some evidence of comparison
---
## Question 11(e):
$92.669 - 92.7$ | B1 | awrt 92.7
---
## Question 11(f):
extrapolation | B1 | Or equivalent; Causation with explanation
It would be an outlier. This model was calculated without outliers. | B1 | Might live in different boroughs than they go to school in; City of London's median would be an outlier compared to other areas; $P=92.67$ with median £61100 with relevant comment; Not many schools in City of London
---
## Question 11(g):
from diagram, percentage is above 50% in all areas and data is for 5 or more passes **including** English and Maths, so there **is** evidence to support this statement | B1 | Not **proves**; All points on scatter graph are above 50% so suggests statement is correct; percentage is above 50% in all areas and data is for 5 or more passes **including English and Maths**, so there is evidence to support this statement11 The pre-release material contains information about the Median Income of Taxpayers and the Percentage of Pupils Achieving at Least 5 A*- C grades, including English and Maths, at the end of KS4 in different areas of London.
Alex is investigating whether there is a relationship between median income and the percentage of pupils achieving at least 5 A* - C grades, including English and Maths, at the end of KS4. Alex decides to use the first 12 rows of data for 2014-5 from the pre-release data as a sample. The sample is shown in Fig. 11.1.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Area & Median Income of Taxpayers & Percentage of Pupils Achieving at Least 5 A*- C grades including English and Maths \\
\hline
City of London & 61100 & \#N/A \\
\hline
Barking and Dagenham & 21800 & 54.0 \\
\hline
Barnet & 27100 & 70.1 \\
\hline
Bexley & 24400 & 55.0 \\
\hline
Brent & 22700 & 60.0 \\
\hline
Bromley & 28100 & 68.0 \\
\hline
Camden & 33100 & 56.4 \\
\hline
Croydon & 25100 & 59.6 \\
\hline
Ealing & 24600 & 62.1 \\
\hline
Enfield & 25300 & 54.5 \\
\hline
Greenwich & 24600 & 57.7 \\
\hline
Hackney & 26000 & 60.4 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 11.1}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Explain whether the data in Fig. 11.1 is a simple random sample of the data for 2014-5.
\item The City of London is included in Alex's sample.
Explain why Alex is not able to use the data for the City of London in this investigation.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Fig. 11.2 shows a scatter diagram showing Percentage of Pupils against Median Income for all of the areas of London for which data is available.}
\includegraphics[alt={},max width=\textwidth]{e0b502a8-c742-4d78-993c-8c0c7329ec9c-09_716_1378_356_244}
\end{center}
\end{figure}
Fig. 11.2
Alex identifies some outliers.
\item On the copy of Fig. 11.2 in the Printed Answer Booklet, ring three of these outliers.
Alex then discards all the outliers and uses the LINEST function on a spreadsheet to obtain the following model.\\
$\mathrm { P } = 0.0009049 \mathrm { M } + 37.38$,\\
where $P =$ percentage of pupils and $M =$ median income.
\item Show that the model is a good fit for the data for Hackney.
\item Use the model to find an estimate of the value of $P$ for City of London.
\item Give two reasons why this estimate may not be reliable.
Alex states that more than 50\% of the pupils in London achieved at least a grade C at the end of KS4 in English and Maths in 2014-5.
\item Use the information in Fig. 11.2 together with your knowledge of the pre-release material to explain whether there is evidence to support this statement.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2022 Q11 [9]}}