| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Calculating stratified sample sizes |
| Difficulty | Easy -1.8 This is a straightforward statistics question testing basic understanding of sampling concepts. Part (a) requires explaining obvious bias (village location affects transport), part (b) is simple arithmetic (107/500 × 60 = 12.84 ≈ 13), and part (c) requires recognizing systematic sampling isn't random. All parts are definitional recall with minimal calculation, well below average A-level difficulty. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Year 7 | Year 8 | Year 9 | Year 10 | Year 11 |
| 86 | 105 | 107 | 101 | 101 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (Probably) wouldn't include any pupils who eg cycle or walk to school (and hence biased towards certain methods of transport) oe | B1 | Must refer to at least one of the given modes of transport |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{107}{500} \times 60\) | M1 | Allow slip in calculation of 500 if clearly their sum of all pupils; may be implied by 12.84 or 12.8 |
| \(13\) | A1 | B2 for 13 unsupported |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Not simple random sampling because every possible sample does not have an equal probability of being selected oe | B1 | Allow: not possible to select every possible sample; every pupil not equally likely to be selected. Do not allow: not simple random sampling because it's systematic sampling |
## Question 9:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| (Probably) wouldn't include any pupils who eg cycle or walk to school (and hence biased towards certain methods of transport) oe | B1 | Must refer to at least one of the given modes of transport |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{107}{500} \times 60$ | M1 | Allow slip in calculation of 500 if clearly their sum of all pupils; may be implied by 12.84 or 12.8 |
| $13$ | A1 | B2 for 13 unsupported |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Not simple random sampling because every possible **sample** does not have an equal probability of being selected oe | B1 | Allow: not possible to select every possible sample; every pupil not equally likely to be selected. Do **not** allow: not simple random sampling because it's systematic sampling |
---9 A teacher is investigating how pupils travel to and from school each day. Pupils can either travel by bus, train, car, bicycle or walk.
The teacher decides to collect a sample of size 60 for the investigation.
\begin{enumerate}[label=(\alph*)]
\item The teacher lives in a village 10 miles away from the school.
Explain how collecting a sample which just consists of pupils who live in the same village as the teacher might introduce bias.
The table below shows how many students there are in each year.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
Year 7 & Year 8 & Year 9 & Year 10 & Year 11 \\
\hline
86 & 105 & 107 & 101 & 101 \\
\hline
\end{tabular}
\end{center}
\item The teacher decides to use the method of proportional stratified sampling.
Calculate the number of pupils in the sample who are in Year 9.
The teacher generates a sample of 10 pupils from the 86 in Year 7 by listing them in alphabetical order and selecting the first name on the list and every ninth name thereafter.
\item Explain whether this method will generate a simple random sample of the pupils who travel in Year 7.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2024 Q9 [4]}}