| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Clean or interpret large data set structure |
| Difficulty | Easy -1.8 This question requires only basic data interpretation skills—reading a table, identifying high/low values, and explaining patterns with common sense reasoning. No calculations, statistical formulas, or mathematical techniques are needed. It's significantly easier than typical A-level questions that require actual computation or application of learned methods. |
| Spec | 2.02i Select/critique data presentation |
| Local Authority | Age 0 to 17 | Age 18 to 24 | Age 25 to 64 | Age 65 and over |
| A | 26.20\% | 9.06\% | 51.81\% | 12.92\% |
| B | 23.32\% | 8.99\% | 52.32\% | 15.37\% |
| C | 22.24\% | 8.96\% | 52.56\% | 16.23\% |
| D | 22.67\% | 8.10\% | 53.27\% | 15.96\% |
| E | 20.70\% | 7.77\% | 54.77\% | 16.76\% |
| F | 18.14\% | 6.51\% | 51.13\% | 24.21\% |
| G | 18.96\% | 14.20\% | 48.51\% | 18.33\% |
| H | 19.06\% | 14.79\% | 52.12\% | 14.04\% |
| I | 25.15\% | 9.04\% | 51.16\% | 14.65\% |
| J | 22.93\% | 8.81\% | 52.22\% | 16.04\% |
| K | 21.48\% | 13.98\% | 50.82\% | 13.73\% |
| L | 23.98\% | 9.20\% | 52.26\% | 14.56\% |
| M | 21.67\% | 11.19\% | 52.94\% | 14.19\% |
| N | 17.82\% | 6.01\% | 51.93\% | 24.23\% |
| O | 22.83\% | 7.30\% | 53.86\% | 16.01\% |
| P | 21.76\% | 8.28\% | 54.03\% | 15.93\% |
| Q | 21.42\% | 8.43\% | 53.90\% | 16.25\% |
| R | 18.61\% | 7.33\% | 49.35\% | 24.71\% |
| Answer | Marks | Guidance |
|---|---|---|
| High(er) or increased proportion 18–24 | B1 [1] | e.g. "many 18–24". Ignore any LA mentioned |
| Answer | Marks | Guidance |
|---|---|---|
| High(er) or increased proportion either/both | B1 [1] | or high proportion of younger. Ignore any LA mentioned |
| Answer | Marks | Guidance |
|---|---|---|
| Low(er) or decreased proportion either/both | B1 [1] | or low proportion of younger. e.g. "LA F because low % in younger ages" B1 |
| Answer | Marks | Guidance |
|---|---|---|
| G, H, K, M | B1 [1] | No extras or omissions |
| Answer | Marks | Guidance |
|---|---|---|
| F, N, R | B1 [1] | No extras or omissions |
| Answer | Marks | Guidance |
|---|---|---|
| Imply need to consider other age range(s); May be a large % of 25–64 (or 65+); Some LAs have low 0–17 and 18–24 and 65+; Low 0–17 & 18–24 does not mean high 65+; Need to consider other factors or anomalies | B1 [1] | Low 0–17 & 18–24 not \(\Rightarrow\) attractive to older. High % of young people does not necessarily imply low % of older people. Older people may want live near young relatives. May be reasons for low % younger people e.g. no schools |
| Answer | Marks | Guidance |
|---|---|---|
| State all 3 LAs are \(> 1.5\times\)IQR above UQ | B1 | Or \(16.76 + 1.5\times(16.76 - 14.56)\) \((= 20.06)\). Ignore attempt at lower limit |
| Confirms F, N, R (implied) despite (c) | B1 [2] | Independent mark. But must mention (c) |
| Answer | Marks | Guidance |
|---|---|---|
| Mean \(>\) UQ | B1* | or mean is in 4th quartile |
| Median better | B1dep [2] | Not Mean skewed by F,N,R so median better. Not Median not skewed by F,N,R so better. Not Mean because need take account of outliers (or F,N,R) |
## Question 10:
**Part (a)(i)**
High(er) or increased proportion 18–24 | **B1** [1] | e.g. "many 18–24". Ignore any LA mentioned
**Part (a)(ii)**
High(er) or increased proportion either/both | **B1** [1] | or high proportion of younger. Ignore any LA mentioned
**Part (a)(iii)**
Low(er) or decreased proportion either/both | **B1** [1] | or low proportion of younger. e.g. "LA F because low % in younger ages" B1
**Part (b)(i)**
G, H, K, M | **B1** [1] | No extras or omissions
**Part (b)(ii)**
F, N, R | **B1** [1] | No extras or omissions
**Part (c)**
Imply need to consider other age range(s); May be a large % of 25–64 (or 65+); Some LAs have low 0–17 and 18–24 and 65+; Low 0–17 & 18–24 does not mean high 65+; Need to consider other factors or anomalies | **B1** [1] | Low 0–17 & 18–24 not $\Rightarrow$ attractive to older. High % of young people does not necessarily imply low % of older people. Older people may want live near young relatives. May be reasons for low % younger people e.g. no schools
**Part (d)**
State all 3 LAs are $> 1.5\times$IQR above UQ | **B1** | Or $16.76 + 1.5\times(16.76 - 14.56)$ $(= 20.06)$. Ignore attempt at lower limit
Confirms F, N, R (implied) despite (c) | **B1** [2] | Independent mark. But must mention (c)
**Part (e)**
Mean $>$ UQ | **B1*** | or mean is in 4th quartile
Median better | **B1**dep [2] | Not Mean skewed by F,N,R so median better. Not Median not skewed by F,N,R so better. Not Mean because need take account of outliers (or F,N,R)
---10 The table shows the age structure of usual residents of 18 Local Authorities (LAs) in the North West region of the UK in 2011.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Local Authority & Age 0 to 17 & Age 18 to 24 & Age 25 to 64 & Age 65 and over \\
\hline
A & 26.20\% & 9.06\% & 51.81\% & 12.92\% \\
\hline
B & 23.32\% & 8.99\% & 52.32\% & 15.37\% \\
\hline
C & 22.24\% & 8.96\% & 52.56\% & 16.23\% \\
\hline
D & 22.67\% & 8.10\% & 53.27\% & 15.96\% \\
\hline
E & 20.70\% & 7.77\% & 54.77\% & 16.76\% \\
\hline
F & 18.14\% & 6.51\% & 51.13\% & 24.21\% \\
\hline
G & 18.96\% & 14.20\% & 48.51\% & 18.33\% \\
\hline
H & 19.06\% & 14.79\% & 52.12\% & 14.04\% \\
\hline
I & 25.15\% & 9.04\% & 51.16\% & 14.65\% \\
\hline
J & 22.93\% & 8.81\% & 52.22\% & 16.04\% \\
\hline
K & 21.48\% & 13.98\% & 50.82\% & 13.73\% \\
\hline
L & 23.98\% & 9.20\% & 52.26\% & 14.56\% \\
\hline
M & 21.67\% & 11.19\% & 52.94\% & 14.19\% \\
\hline
N & 17.82\% & 6.01\% & 51.93\% & 24.23\% \\
\hline
O & 22.83\% & 7.30\% & 53.86\% & 16.01\% \\
\hline
P & 21.76\% & 8.28\% & 54.03\% & 15.93\% \\
\hline
Q & 21.42\% & 8.43\% & 53.90\% & 16.25\% \\
\hline
R & 18.61\% & 7.33\% & 49.35\% & 24.71\% \\
\hline
\end{tabular}
\end{center}
\section*{Percentage of residents}
\begin{enumerate}[label=(\alph*)]
\item Without reference to any other columns, explain how you would use only the columns for the age ranges 0 to 17 and 18 to 24 to decide whether an LA might be one of the following.
\begin{enumerate}[label=(\roman*)]
\item An LA that includes a university
\item An LA that attracts young couples to live
\item An LA that attracts retired people to live
\end{enumerate}\item Using your answers to part (a), identify the following.
\begin{enumerate}[label=(\roman*)]
\item Four LAs that might include a university
\item Three LAs that might be attractive to retired people
\end{enumerate}\item Explain why your answer to part (b)(ii), based only on the columns for the age ranges 0 to 17 and 18 to 24, may not be reliable.
\item The lower quartile, median and upper quartile of the percentages in the column "Age 65 and over" are $14.56 \% , 15.99 \%$ and $16.76 \%$ respectively.
Use this information to comment on your answers to part (b)(ii) and part (c).
In a magazine article, a councillor plans to describe a typical LA in the North West region. He wants to quote the average percentage of residents aged 65 or over.
\item The mean of the percentages in the column "Age 65 and over" is $16.90 \%$.
Use this information, and the information given in part (d), to explain whether the median or the mean better represents the data in the column "Age 65 and over".
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2022 Q10 [10]}}