| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2021 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Select random sample using random numbers |
| Difficulty | Easy -1.8 This is a very straightforward question testing basic understanding of sampling bias and simple random number extraction. Part (a) requires only recognizing obvious sampling bias (students at music building are not representative). Part (b) is purely mechanical: reading consecutive digits from random numbers and rejecting those outside 1-256, requiring no mathematical reasoning beyond basic number recognition. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| E.g. Bias towards students who play instruments or only music students, or e.g. the six will possibly be friends/have similar music preferences | B1 | OE. Or any reason that some are excluded e.g. because it is lunchtime or because the music building is chosen, or any suggestion that opinions may not be independent. Note: 'not representative of all students' needs qualifying |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 28, 119, 207 | B1 | B1 for 28, 119 (condone 028) |
| B1 | B1 for 207 and only 3 values stated | |
| 2 |
## Question 2:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| E.g. Bias towards students who play instruments or only music students, or e.g. the six will possibly be friends/have similar music preferences | B1 | OE. Or any reason that some are excluded e.g. because it is lunchtime or because the music building is chosen, or any suggestion that opinions may not be independent. Note: 'not representative of all students' needs qualifying |
| | **1** | |
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 28, 119, 207 | **B1** | **B1** for 28, 119 (condone 028) |
| | **B1** | **B1** for 207 and only 3 values stated |
| | **2** | |
---2 Andy and Jessica are doing a survey about musical preferences. They plan to choose a representative sample of six students from the 256 students at their college.
\begin{enumerate}[label=(\alph*)]
\item Andy suggests that they go to the music building during the lunch hour and choose six students at random from the students who are there.
Give a reason why this method is unsatisfactory.
\item Jessica decides to use another method. She numbers all the students in the college from 1 to 256. Then she uses her calculator and generates the following random numbers.
$$\begin{array} { l l l l l }
204393 & 162007 & 204028 & 587119 & 207395
\end{array}$$
From these numbers, she obtains six student numbers. The first three of her student numbers are 204, 162 and 7.
Continue Jessica's method to obtain the next three student numbers.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2021 Q2 [3]}}