| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Implementing simple random or systematic sampling |
| Difficulty | Easy -1.8 This is a purely descriptive question testing basic definitions and procedures for random sampling. It requires no calculations, no problem-solving, and no mathematical insight—only recall of standard textbook definitions and the mechanical procedure for using random number tables. This is significantly easier than typical A-level questions that require applying techniques to solve problems. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| This is a sample where every (possible) sample (of size \(n\)) has an equal chance of being chosen. | B1 | Require all / each / every etc sample and same/equal etc chance / probability for B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| 'When it is impossible to provide a sampling frame' or a correct example with an indication of sampling frame being impossible. | B1 | Require impossible / no / doesn't exist etc and sampling frame for B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| A list/register of all the students. | B1 | Require list/register etc and all/every/75 etc students for B1; List of 8 students is B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Number the students (from 0 to 74, 1 to 75 etc.) | B1 | First B1 accept 'in the corresponding position' o.e. if numbering omitted |
| Using the random no. table read off the nos. and identify or select the students allocated those nos. | B1 | Second B1 require both for mark |
## Question 1:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| This is a sample where **every** (possible) **sample** (of size $n$) has an **equal chance** of being chosen. | B1 | Require **all / each / every** etc **sample** and **same/equal** etc **chance / probability** for B1 |
**(1 mark)**
---
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| 'When it is impossible to provide a **sampling frame**' or a correct example with an indication of sampling frame being impossible. | B1 | Require **impossible / no / doesn't exist** etc and **sampling frame** for B1 |
**(1 mark)**
---
### Part (c)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| A **list/register** of **all** the students. | B1 | Require **list/register** etc and **all/every/75** etc students for B1; List of 8 students is B0 |
---
### Part (c)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Number the students (from 0 to 74, 1 to 75 etc.) | B1 | First B1 accept **'in the corresponding position' o.e.** if numbering omitted |
| Using the **random no. table** read off the nos. and **identify or select the students allocated those nos**. | B1 | Second B1 require both for mark |
**(3 marks)**
**Total: 5 marks**\begin{enumerate}
\item (a) Explain what you understand by a random sample from a finite population.\\
(b) Give an example of a situation when it is not possible to take a random sample.
\end{enumerate}
A college lecturer specialising in shoe design wants to change the way in which she organises practical work.
She decides to gather ideas from her 75 students.
She plans to give a questionnaire to a random sample of 8 of these students.\\
(c) (i) Describe the sampling frame that she should use.\\
(ii) Explain in detail how she should use a table of random numbers to obtain her sample.\\
\hfill \mbox{\textit{Edexcel S3 2014 Q1 [5]}}