| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Identify and compare sampling techniques |
| Difficulty | Easy -1.2 This question tests basic sampling terminology (opportunity sampling), simple definitions (why it's not random), and straightforward histogram-to-frequency table conversions using frequency density. Part (d) requires reading histogram bars and calculating a simple probability. All parts are recall or direct application of standard techniques with no problem-solving or novel insight required—significantly easier than average A-level questions. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.02b Histogram: area represents frequency |
| Weight in kg | \(50 -\) | \(65 -\) | \(75 -\) | \(80 -\) | \(90 -\) | \(100 - 120\) |
| Frequency | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| Opportunity/Convenience sampling | B1 | Condone 'Opportunistic Sampling' |
| Answer | Marks | Guidance |
|---|---|---|
| Because every sample (of size \(n\)) does not have the same probability of being selected | B1 | Accept 'all adult males registered at the surgery do not have an equal chance of being selected'. OR 'For a SRS each element from the SF must have an equal chance of selection'. OR 'A subset of the population cannot form a complete sampling frame'. OR 'The sampling frame would be incomplete'. Note: 'No random method employed' is B0; 'Only collected data from one week' is B0. |
| Answer | Marks | Guidance |
|---|---|---|
| w | 50- | 65- |
| f | 6 | 8 |
| B1 | AO 1.1 | — |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{2}{3} \times \text{their } 6 + \frac{1}{2} \times \text{their } 6\) or \((10 \times 0.4) + (10 \times 0.3)\) | M1 | AO 1.1 |
| \(\frac{7}{45}\) or \(0.1\dot{5}\) or \(0.15555\) to \(0.156\); Mark at most accurate | A1FT | AO 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| The distribution of the weights within each class is unknown | E1 | AO 2.4 |
## Question 12:
### Part (a):
Opportunity/Convenience sampling | **B1** | Condone 'Opportunistic Sampling'
### Part (b):
Because every sample (of size $n$) does not have the same probability of being selected | **B1** | Accept 'all adult males registered at the surgery do not have an equal chance of being selected'. OR 'For a SRS each element from the SF must have an equal chance of selection'. OR 'A subset of the population cannot form a complete sampling frame'. OR 'The sampling frame would be incomplete'. Note: 'No random method employed' is B0; 'Only collected data from one week' is B0.
## Question 12:
### Part (c):
| w | 50- | 65- | 70- | 80- | 90- | 100-120 |
|---|-----|-----|-----|-----|-----|---------|
| f | 6 | 8 | 8 | 11 | 6 | 6 |
**B1** | AO 1.1 | —
### Part (d):
$\frac{2}{3} \times \text{their } 6 + \frac{1}{2} \times \text{their } 6$ or $(10 \times 0.4) + (10 \times 0.3)$ | **M1** | AO 1.1 | If part (c) correct, implied by '4+3'
$\frac{7}{45}$ or $0.1\dot{5}$ or $0.15555$ to $0.156$; Mark at most accurate | **A1FT** | AO 1.1 | FT their 6, 6 and 45. May need to check calculation. May see interpolation methods, which lead to the same calc.
### Part (e):
The distribution of the weights within each class is unknown | **E1** | AO 2.4 | Accept 'we assume that the values (individual weights) are equally distributed in each class interval'; Accept 'the individual values (weights) are not known'; Accept 'the number of people (frequency) in each category of the histogram may not be spread out equally across the category'; Accept 'we don't know exactly how many were less than 60kg and how many were more than 110kg'
---12 Doctors are investigating the weights of adult males registered at their surgery. One week they collect a sample by noting the weight in kilograms of all the adult males who have an appointment at their surgery.
\begin{enumerate}[label=(\alph*)]
\item State the sampling method they use.
\item Explain why this method will not generate a simple random sample of all the adult males registered at their surgery.
They represent the data using a histogram.\\
\includegraphics[max width=\textwidth, alt={}, center]{82438df0-6550-4ffd-92d8-3c67bec59a6b-09_1166_1243_726_233}
An incomplete frequency table for the data is shown below.
\begin{center}
\begin{tabular}{ | l | l | c | l | l | l | l | }
\hline
Weight in kg & $50 -$ & $65 -$ & $75 -$ & $80 -$ & $90 -$ & $100 - 120$ \\
\hline
Frequency & & 8 & & & & \\
\hline
\end{tabular}
\end{center}
\item Complete the copy of the frequency table in the Printed Answer Booklet.
One of these patients is selected at random.
\item Determine an estimate of the probability that he weighs either less than 60 kg or more than 110 kg .
\item Explain why your answer to part (d) is an estimate and not exact.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2023 Q12 [6]}}