| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Non-parametric tests |
| Type | Systematic sampling methods |
| Difficulty | Easy -1.8 This is a straightforward question testing basic understanding of systematic sampling mechanics. Part (a) requires simple recall (divide 400 by 8, pick random start, add 50 repeatedly), part (b) needs a standard disadvantage (e.g., alphabetical ordering bias), and part (c) is trivial arithmetic (probability is 0 since 001 and 400 cannot both be in a systematic sample with interval 50). No problem-solving or mathematical manipulation required—pure procedural recall. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Select a random number as the starting point | B1 | B1 for realising they need to select a random number as the starting point |
| Take every \(50^{th}\) employee | B1 | B1 for realising they need to take every \(50^{th}\) employee |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| e.g. The alphabetical list may not be random or may be biased as list not truly random or some combinations of names are not possible | B1 | B1 for a suitable disadvantage. Sight of the words in bold oe for those reasons are sufficient, provided there is no contradiction or not a correct reason. Condone "may not be representative" / "some employees with the same surname won't be chosen". Do not allow any reference to requiring a sampling frame as it already has one e.g. "a sampling frame is needed because there is an alphabetical list" |
| (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(0\) | B1 | B1 for answer of \(0\) |
| (1) | ||
| Total: 4 |
## Question 1:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Select a random number as the starting point | B1 | B1 for realising they need to select a random number as the starting point |
| Take every $50^{th}$ employee | B1 | B1 for realising they need to take every $50^{th}$ employee |
| | **(2)** | |
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| e.g. The alphabetical list may not be **random** or may be **biased** as list not truly random or some **combinations** of names are **not possible** | B1 | B1 for a suitable disadvantage. Sight of the words in bold oe for those reasons are sufficient, provided there is no contradiction or not a correct reason. Condone "may not be representative" / "some employees with the same surname won't be chosen". Do not allow any reference to requiring a sampling frame as it already has one e.g. "a sampling frame is needed because there is an alphabetical list" |
| | **(1)** | |
### Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| $0$ | B1 | B1 for answer of $0$ |
| | **(1)** | |
| | **Total: 4** | |\begin{enumerate}
\item The names of the 400 employees of a company are listed alphabetically in a book.
\end{enumerate}
The chairperson of the company wishes to select a sample of 8 employees.\\
The chairperson numbers the employees from 001 to 400\\
(a) Describe how the list of numbers can be used to select a systematic sample of 8 employees.\\
(b) State one disadvantage of systematic sampling in this case.\\
(c) Write down the probability that the sample includes both the first name (employee 001) and the last name (employee 400) in the list.
\hfill \mbox{\textit{Edexcel S3 2024 Q1 [4]}}