| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2022 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Non-parametric tests |
| Type | Systematic sampling methods |
| Difficulty | Easy -1.2 This is a straightforward question testing basic understanding of sampling methods with no calculations required. Students only need to recall definitions and explain standard advantages/disadvantages of systematic vs simple random vs stratified sampling. The numerical context (1200/60, 200 students) requires minimal arithmetic to recognize the stratification issue. This is considerably easier than average A-level maths questions which typically require multi-step problem-solving or technical manipulation. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| Number the 1200 students (\(1 - 1200\)) | B1 | Numbering the students (Allow \(0 - 1199\)) |
| Use a random starting point between 1 and 20 | B1 | Using a random starting point. Must be between 1 and 20 (Allow \(0 - 19\)) |
| Select every \(20^{th}\) person on the list | B1 | Selecting every \(20^{th}\) person |
| (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| They only need to generate one random number | B1 | A suitable comment |
| (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| It is not random as the list is ordered alphabetically or not all combinations of sampling units are possible | M1 | A suitable comment |
| e.g. unlikely siblings would be selected | A1 | A suitable example |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| Number of Y9 students \(= \dfrac{200}{1200} \times 60 \ [= 10]\) | M1 | A suitable calculation to find the number of Y9 students e.g. \(\dfrac{200}{1200} \times 60\) |
| The stratified sample gives a better proportion or is more representative oe | A1 | A correct explanation |
| (2) |
## Question 1:
### Part (a)
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| Number the 1200 students ($1 - 1200$) | B1 | Numbering the students (Allow $0 - 1199$) |
| Use a random starting point between 1 and 20 | B1 | Using a random starting point. Must be between 1 and 20 (Allow $0 - 19$) |
| Select every $20^{th}$ person on the list | B1 | Selecting every $20^{th}$ person |
| | **(3)** | |
### Part (b)(i)
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| They only need to generate one random number | B1 | A suitable comment |
| | **(1)** | |
### Part (b)(ii)
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| It is not random as the list is ordered alphabetically **or** not all combinations of sampling units are possible | M1 | A suitable comment |
| e.g. unlikely siblings would be selected | A1 | A suitable example |
| | **(2)** | |
### Part (c)
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| Number of Y9 students $= \dfrac{200}{1200} \times 60 \ [= 10]$ | M1 | A suitable calculation to find the number of Y9 students e.g. $\dfrac{200}{1200} \times 60$ |
| The stratified sample gives a better proportion or is more representative oe | A1 | A correct explanation |
| | **(2)** | |
**Total: 8 marks**\begin{enumerate}
\item The Headteacher of a school is thinking about making changes to the school day. She wants to take a sample of 60 students so that she can find out what the students think about the proposed changes.
\end{enumerate}
The names of the 1200 students of the school are listed alphabetically.\\
(a) Explain how the Headteacher could take a systematic sample of 60 students.\\
(b) (i) Explain why systematic sampling is likely to be quicker than simple random sampling in this situation.\\
(ii) With reference to this situation,
\begin{itemize}
\item explain why systematic sampling may introduce bias compared to simple random sampling
\item give an example of the bias that may occur when using this alphabetical list
\end{itemize}
When the Headteacher completes the systematic sample of size 60 she finds that 6 students were to be selected from Year 9.
The Head of Mathematics suggests that a stratified sample of size 60 would be a more appropriate method.
There were 200 students in Year 9.\\
(c) Explain why this suggests that a stratified sample of size 60 may be better than the systematic sample taken by the Headteacher.
\hfill \mbox{\textit{Edexcel S3 2022 Q1 [8]}}