| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2021 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Implementing simple random or systematic sampling |
| Difficulty | Easy -1.8 This is a straightforward procedural question on basic sampling methods requiring only mechanical application of random number tables and simple stratified sampling calculations. No problem-solving, conceptual understanding, or mathematical reasoning is needed—just following standard S3 procedures that would be directly taught and practiced. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| In QP: 33, 15, 23 → 29, 34, 39, 06, 31, 13, 42 | M1A1 | M1 for 7 numbers (at least 4 correct in any order). Condone repeats but only count once towards the "4". A1 for all 7 correct with no repeats |
| 4 girls: 15, 23, 06, 13; 6 boys: 33, 29, 34, 39, 31, 42 | B1, B1 | 1st B1 for showing 4 girls in sample (no ft for incorrect random numbers); 2nd B1 for showing 6 boys in sample (no ft for incorrect random numbers) |
| Highest number is 42 → therefore may miss older players | M1, A1 | M1 for mention of highest number 42 (or if their highest number is as long as < 60); A1 for stating that this means older players may be missing from the sample. Can be awarded if highest number is stated for M1 and is < 42 |
| Answer/Working | Marks | Guidance |
|---|---|---|
| In QP: 33, 15, 23 → 29, 34, 39, 06, 31, 13, 42 | M1A1 | M1 for 7 numbers (at least 4 correct in any order). Condone repeats but only count once towards the "4". A1 for all 7 correct with no repeats |
| 4 girls: 15, 23, 06, 13; 6 boys: 33, 29, 34, 39, 31, 42 | B1, B1 | 1st B1 for showing 4 girls in sample (no ft for incorrect random numbers); 2nd B1 for showing 6 boys in sample (no ft for incorrect random numbers) |
| Highest number is 42 → therefore may miss older players | M1, A1 | M1 for mention of highest number 42 (or if their highest number is as long as < 60); A1 for stating that this means older players may be missing from the sample. Can be awarded if highest number is stated for M1 and is < 42 |
**Total: [6 marks]**
---\begin{enumerate}
\item A journalist is going to interview a sample of 10 players from the 60 players in a local football club. The journalist uses the random numbers on page 27 of the formula booklet and starts at the top of the 10th column, where the first number is 96
\end{enumerate}
The journalist worked down the 10th column to select 10 numbers. The first 3 numbers selected were: 33, 15 and 23\\
(a) Find the other 7 numbers to complete the sample of ten.
There are 24 girls and 36 boys who play football for the club.\\
The journalist labels the girls from 1 to 24 and the boys from 25 to 60\\
(b) Show how the journalist can use her 10 random numbers to select a stratified sample of 10 players from the club to interview.
The club provided the journalist with a list of the players in ascending order of ages, numbered 1 to 60. The journalist uses the 10 random numbers to select a simple random sample of the players.\\
(c) State, giving a reason, a group of players who may not be represented in this sample.\\
\hfill \mbox{\textit{Edexcel S3 2021 Q1 [6]}}