CAIE S1 2021 November — Question 6 10 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2021
SessionNovember
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicData representation
TypeDraw back-to-back stem-and-leaf diagram
DifficultyEasy -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.
Spec2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread

6 The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below.
Rebels7578798082828384858689939599102
Sharks666871727475757678838384858692
  1. Represent the data by drawing a back-to-back stem-and-leaf diagram with Rebels on the left-hand side of the diagram.
  2. 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}
  3. On the same diagram, draw a box-and-whisker plot for the Rebels.
  4. Make one comparison between the weights of the players in the Rebels club and the weights of the players in the Sharks club.

Question 6(a):
AnswerMarks Guidance
AnswerMarks Guidance
Correct stemB1 Correct stem, ignore extra values (not in reverse)
Rebels leaves in order from right to left, lined up vertically, no commasB1 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 commasB1 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
Question 6(b):
AnswerMarks Guidance
AnswerMarks 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):
AnswerMarks Guidance
AnswerMarks Guidance
Box and whisker with end points 75 and 102B1 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):
AnswerMarks Guidance
AnswerMarks Guidance
e.g. Average weight of Rebels is higher than average weight of SharksB1 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]}}