| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2021 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw back-to-back stem-and-leaf diagram |
| Difficulty | Easy -1.3 This is a straightforward data representation question requiring routine construction of a back-to-back stem-and-leaf diagram from ordered data, calculation of standard summary statistics (median and IQR), and drawing a box plot. All data is already sorted, requiring only organizational skills rather than problem-solving or conceptual understanding. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Rebels | 75 | 78 | 79 | 80 | 82 | 82 | 83 | 84 | 85 | 86 | 89 | 93 | 95 | 99 | 102 |
| Sharks | 66 | 68 | 71 | 72 | 74 | 75 | 75 | 76 | 78 | 83 | 83 | 84 | 85 | 86 | 92 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct stem | B1 | Correct stem, ignore extra values (not in reverse) |
| Rebels leaves in order from right to left, lined up vertically, no commas | B1 | Correct Rebels labelled on left, leaves in order from right to left and lined up vertically, no commas |
| Sharks leaves in order, lined up vertically, no commas | B1 | Correct Sharks labelled on same diagram, leaves in order and lined up vertically, no commas |
| Key: \(8 \ | 7 \ | 2\) means 78 kg for Rebels and 72 kg for Sharks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 84\) (kg) | B1 | |
| \([\text{UQ} = 93, \text{LQ} = 80]\ 93 - 80\) | M1 | \(95 \leqslant \text{UQ} \leqslant 89 - 79 \leqslant \text{LQ} \leqslant 82\) |
| \([\text{IQR} =]\ 13\) (kg) | A1 | WWW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Box and whisker with end points 75 and 102 | B1 | Whiskers drawn to correct end points not through box, not joining at top or bottom of box |
| Median and quartiles plotted as found in (b) | B1 FT | Quartiles and median plotted as box graph |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. Average weight of Rebels is higher than average weight of Sharks | B1 | Acceptable answers refer to: Range, skew, central tendency within context. E.g. range of Rebels is greater B0. Range of weights of the rebels is greater B1. Simple value comparison insufficient |
## Question 6(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct stem | B1 | Correct stem, ignore extra values (not in reverse) |
| Rebels leaves in order from right to left, lined up vertically, no commas | B1 | Correct Rebels labelled on left, leaves in order from right to left and lined up vertically, no commas |
| Sharks leaves in order, lined up vertically, no commas | B1 | Correct Sharks labelled on same diagram, leaves in order and lined up vertically, no commas |
| Key: $8 \| 7 \| 2$ means 78 kg for Rebels and 72 kg for Sharks | B1 | Correct key for their diagram, need both teams identified and 'kg' stated at least once here or in leaf headings or title. **SC** If 2 separate diagrams drawn, **SC B1** if both keys meet these criteria |
---
## Question 6(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 84$ (kg) | B1 | |
| $[\text{UQ} = 93, \text{LQ} = 80]\ 93 - 80$ | M1 | $95 \leqslant \text{UQ} \leqslant 89 - 79 \leqslant \text{LQ} \leqslant 82$ |
| $[\text{IQR} =]\ 13$ (kg) | A1 | WWW |
---
## Question 6(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Box and whisker with end points 75 and 102 | B1 | Whiskers drawn to correct end points not through box, not joining at top or bottom of box |
| Median and quartiles plotted as found in **(b)** | B1 FT | Quartiles and median plotted as box graph |
---
## Question 6(d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. Average weight of Rebels is higher than average weight of Sharks | B1 | Acceptable answers refer to: Range, skew, central tendency within context. E.g. range of Rebels is greater **B0**. Range of weights of the rebels is greater **B1**. Simple value comparison insufficient |
6 The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Rebels & 75 & 78 & 79 & 80 & 82 & 82 & 83 & 84 & 85 & 86 & 89 & 93 & 95 & 99 & 102 \\
\hline
Sharks & 66 & 68 & 71 & 72 & 74 & 75 & 75 & 76 & 78 & 83 & 83 & 84 & 85 & 86 & 92 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Represent the data by drawing a back-to-back stem-and-leaf diagram with Rebels on the left-hand side of the diagram.
\item Find the median and the interquartile range for the Rebels.\\
A box-and-whisker plot for the Sharks is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{a2709c37-6e81-4873-8f38-94cb9f3c3252-09_533_1246_388_445}
\item On the same diagram, draw a box-and-whisker plot for the Rebels.
\item Make one comparison between the weights of the players in the Rebels club and the weights of the players in the Sharks club.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2021 Q6 [10]}}