| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Describe or suggest sampling method |
| Difficulty | Easy -1.3 This is a straightforward sampling question requiring recall of stratified sampling advantages and basic proportional calculations. Part (a) is definitional recall, part (b) involves simple arithmetic (finding proportions of 40), and part (c) requires describing a standard procedure. No problem-solving or novel insight needed—well below average difficulty. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Any one of: accurate estimates for each strata/job; more representative of the population; reflects population structure | B1 | Any 1 or equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Total staff \(= 720\) | B1 | May be implied by calculations |
| \(\text{Managers} = \frac{72}{720} \times 40 = 4\) | M1 | For one correct calculation, follow through their 720 |
| \(\text{Drivers} = \frac{108}{720} \times 40 = 6\) | ||
| \(\text{Administrators} = \frac{180}{720} \times 40 = 10\) | ||
| \(\text{Warehouse} = \frac{360}{720} \times 40 = 20\) | A1 | Values 4, 6, 10, 20 only. Must identify which job the values relate to |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Label all managers \(1 - 72\) o.e. | B1 | Idea of sampling frame or list of managers. Need not give the specific term |
| Using random numbers in range \(1\)-\(72\) or \(0\)-\(71\), select 4 managers | B1 | Use of random numbers to select required number of managers. Must mention use of random numbers or some random selection process. If describing systematic sampling score B0 |
## Question 1:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Any one of: accurate estimates for each strata/job; more representative of the population; reflects population structure | B1 | Any 1 or equivalent |
**(1 mark)**
---
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Total staff $= 720$ | B1 | May be implied by calculations |
| $\text{Managers} = \frac{72}{720} \times 40 = 4$ | M1 | For one correct calculation, follow through their 720 |
| $\text{Drivers} = \frac{108}{720} \times 40 = 6$ | | |
| $\text{Administrators} = \frac{180}{720} \times 40 = 10$ | | |
| $\text{Warehouse} = \frac{360}{720} \times 40 = 20$ | A1 | Values 4, 6, 10, 20 only. Must identify which job the values relate to |
**(3 marks)**
---
### Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Label all managers $1 - 72$ o.e. | B1 | Idea of **sampling frame** or **list** of managers. Need not give the specific term |
| Using random numbers in range $1$-$72$ or $0$-$71$, select 4 managers | B1 | Use of **random numbers** to select required number of managers. Must mention use of random numbers or some **random** selection process. If describing systematic sampling score B0 |
**(2 marks)**
**Total: 6 marks**\begin{enumerate}
\item A company director decides to survey staff about changes to the company calendar. The company has staff in 4 different job roles
\end{enumerate}
72 managers, 108 drivers, 180 administrators and 360 warehouse staff.\\
The director decides to take a stratified sample.\\
(a) Write down one advantage of using a stratified sample rather than a simple random sample for this survey.\\
(b) Find the number of staff in each job role that will be included in a stratified sample of 40 staff.\\
(c) Describe how to choose managers for the stratified sample.
\hfill \mbox{\textit{Edexcel S3 2017 Q1 [6]}}