| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Compare distributions using stem-and-leaf |
| Difficulty | Easy -1.2 This is a straightforward stem-and-leaf question requiring basic statistical skills: reading the diagram, finding median/IQR by counting positions, and using the mean formula. All techniques are routine recall with no problem-solving insight needed, making it easier than average. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Cheetahs | Panthers | ||||||||||
| 9 | 8 | 7 | 4 | ||||||||
| 8 | 7 | 3 | 2 | 0 | 8 | 6 | 8 | ||||
| 9 | 8 | 7 | 9 | 1 | 7 | 8 | 9 | 9 | |||
| 6 | 5 | 3 | 3 | 1 | 10 | 2 | 3 | 4 | 4 | 5 | 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Median \(= 99\) [minutes] | B1 | |
| \([\text{IQR} =] \ 106 - 83\) | M1 | \(105 \leq UQ \leq 112 - 82 \leq LQ \leq 87\) |
| 23 [minutes] | A1 | www. If M0 scored SC B1 for 23 www |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The times for the Cheetahs are faster than the times for the Panthers | B1 | Correct statement comparing central tendency in context |
| The times for the Cheetahs are more spread than the times for the Panthers | B1 | Correct statement comparing range/IQR in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| [Total time including Kenny \(= 99 \times 20 =\)] 1980 | B1 | Accept unsimplified |
| [Kenny's time \(=\)] \(1980 - 1862\) | M1 | For their \(1980 -\) their \(1862\) |
| \(= 118\) [minutes] | A1 | Accept 1 hour 58 mins |
| Alternative: \(\frac{1862 + \text{their Kenny's time}}{20} = 99\); Kenny's time \(= 99\times20 - 1862\) | B1, M1 | \(\frac{1862+\text{their Kenny's time}}{20}=99\) seen; for their \(99\times20 -\) their \(1862\) |
| \(= 118\) [minutes] | A1 | Accept 1 hour 58 mins |
## Question 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Median $= 99$ [minutes] | B1 | |
| $[\text{IQR} =] \ 106 - 83$ | M1 | $105 \leq UQ \leq 112 - 82 \leq LQ \leq 87$ |
| 23 [minutes] | A1 | www. If M0 scored SC B1 for 23 www |
---
## Question 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| The times for the Cheetahs are faster than the times for the Panthers | B1 | Correct statement comparing central tendency in context |
| The times for the Cheetahs are more spread than the times for the Panthers | B1 | Correct statement comparing range/IQR in context |
---
## Question 4(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| [Total time including Kenny $= 99 \times 20 =$] 1980 | B1 | Accept unsimplified |
| [Kenny's time $=$] $1980 - 1862$ | M1 | For their $1980 -$ their $1862$ |
| $= 118$ [minutes] | A1 | Accept 1 hour 58 mins |
| **Alternative:** $\frac{1862 + \text{their Kenny's time}}{20} = 99$; Kenny's time $= 99\times20 - 1862$ | B1, M1 | $\frac{1862+\text{their Kenny's time}}{20}=99$ seen; for their $99\times20 -$ their $1862$ |
| $= 118$ [minutes] | A1 | Accept 1 hour 58 mins |
---4 The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the following back-to-back stem-and-leaf diagram.
\begin{center}
\begin{tabular}{ c c c c c | c | c c c c c c }
\multicolumn{4}{c|}{Cheetahs} & \multicolumn{7}{|c}{Panthers} & \\
\hline
& & & 9 & 8 & 7 & 4 & & & & & \\
8 & 7 & 3 & 2 & 0 & 8 & 6 & 8 & & & & \\
& & 9 & 8 & 7 & 9 & 1 & 7 & 8 & 9 & 9 & \\
6 & 5 & 3 & 3 & 1 & 10 & 2 & 3 & 4 & 4 & 5 & 6 \\
\end{tabular}
\end{center}
Key: 7 |9| 1 means 97 minutes for Cheetahs and 91 minutes for Panthers
\begin{enumerate}[label=(\alph*)]
\item Find the median and the interquartile range of the times of the Cheetahs.\\
The median and interquartile range for the Panthers are 103 minutes and 14 minutes respectively.
\item Make two comparisons between the times taken by the Cheetahs and the times taken by the Panthers.\\
Another cyclist, Kenny, from the Cheetahs also took part in the race. The mean time taken by the 20 cyclists from the Cheetahs was 99 minutes.
\item Find the time taken by Kenny to complete the race.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2023 Q4 [8]}}