| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| 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 and box plot from given data. The skills are purely mechanical (organizing data, finding five-number summary) with no problem-solving or conceptual depth—standard GCSE/AS-level statistics practice that's easier than typical A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02i Select/critique data presentation |
| Penguins | 35 | 39 | 42 | 44 | 45 | 45 | 48 | 50 | 56 | 58 | 59 | 61 | 66 | 68 | 72 |
| Dolphins | 36 | 41 | 43 | 48 | 49 | 49 | 50 | 51 | 54 | 56 | 56 | 60 | 61 | 64 | 71 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stem correct (3,4,5,6,7) | B1 | Correct stem, ignore extra values (not in reverse, not split). If split stem-and-leaf plot used, remaining B marks available |
| Penguins: 9 5 \ | 3 \ | ..., 8 5 5 4 2 \ |
| Dolphins: 6 \ | 3, 1 3 8 9 9 \ | 4, 0 1 4 6 6 \ |
| Key: 2\ | 4\ | 1 means 42 seconds for Penguins and 41 seconds for Dolphins |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For Dolphins, median is 51 | B1 | Plotted on box |
| \(LQ = 48,\ UQ = 60\) | B1 | Plotted on box |
| Correct end points of whiskers and diagram labelled Dolphins | B1 | Correct end points of whiskers (36 and 71). Whiskers not through box, not drawn at corners of boxes, diagram labelled |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Dolphins have more consistent times than Penguins or Penguins are faster (have faster times) than Dolphins | B1 | Reason given in context. Can be reference to either the central tendency or spread |
# Question 4:
## Part 4(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stem correct (3,4,5,6,7) | B1 | Correct stem, ignore extra values (not in reverse, not split). If split stem-and-leaf plot used, remaining B marks available |
| Penguins: 9 5 \| 3 \| ..., 8 5 5 4 2 \| 4 \| ..., 9 8 6 0 \| 5 \| ..., 8 6 1 \| 6 \| ..., 2 \| 7 \| ... (leaves right to left, lined up) | B1 | Correct Penguins labelled on left, leaves in order from right to left and lined up vertically, no commas or punctuation |
| Dolphins: 6 \| 3, 1 3 8 9 9 \| 4, 0 1 4 6 6 \| 5, 0 1 4 \| 6, 1 \| 7 (leaves in order) | B1 | Correct Dolphins labelled on same diagram, leaves in order and lined up vertically, no commas or punctuation |
| Key: 2\|4\|1 means 42 seconds for Penguins and 41 seconds for Dolphins | B1 | Correct key for their diagram, need both clubs labelled and 'sec' or 's' stated at least once, or in leaf headings or title |
## Part 4(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| For Dolphins, median is 51 | B1 | Plotted on box |
| $LQ = 48,\ UQ = 60$ | B1 | Plotted on box |
| Correct end points of whiskers and diagram labelled Dolphins | B1 | Correct end points of whiskers (36 and 71). Whiskers not through box, not drawn at corners of boxes, diagram labelled |
## Part 4(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Dolphins have more consistent times than Penguins **or** Penguins are faster (have faster times) than Dolphins | B1 | Reason given in context. Can be reference to either the central tendency or spread |4 The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the following table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Penguins & 35 & 39 & 42 & 44 & 45 & 45 & 48 & 50 & 56 & 58 & 59 & 61 & 66 & 68 & 72 \\
\hline
Dolphins & 36 & 41 & 43 & 48 & 49 & 49 & 50 & 51 & 54 & 56 & 56 & 60 & 61 & 64 & 71 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a back-to-back stem-and-leaf diagram to represent this information, with Penguins on the left-hand side.\\
\includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-09_2720_33_141_20}
The diagram shows a box-and-whisker plot representing the times for the Penguins.
\item On the same diagram, draw a box-and-whisker plot to represent the times for the Dolphins.\\
\includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-09_719_1219_424_424}
\item Hence state one difference between the distributions of the times for the Penguins and the Dolphins.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2024 Q4 [8]}}