| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Linear programming and optimization |
| Difficulty | Easy -1.8 This is a straightforward systematic sampling question requiring only basic division (720รท40=18) and understanding of the definition. Parts (a)-(c) are pure arithmetic recall with no problem-solving, and part (d) asks for standard textbook advantages/disadvantages of systematic sampling. Significantly easier than average A-level maths. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 57 | 64.61 |
Question 1:
1 | 57 | 64.61 | 57 | 64.61 | 0.8963 | 50.2863The names of the 720 members of a swimming club are listed alphabetically in the club's membership book. The chairman of the swimming club wishes to select a systematic sample of 40 names. The names are numbered from 001 to 720 and a number between 001 and $w$ is selected at random. The corresponding name and every $x$th name thereafter are included in the sample.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $w$. [1]
\item Find the value of $x$. [1]
\item Write down the probability that the sample includes both the first name and the second name in the club's membership book. [1]
\item State one advantage and one disadvantage of systematic sampling in this case. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2015 Q1 [5]}}