| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2023 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct back-to-back stem-and-leaf from raw data |
| Difficulty | Easy -1.8 This is a routine data handling exercise requiring only basic skills: organizing data into a stem-and-leaf diagram, finding median and IQR from ordered data (standard formulas with n=11), and making a simple comparison. No problem-solving or conceptual depth required—purely mechanical application of basic statistical techniques. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Aces | 180 | 174 | 169 | 182 | 181 | 166 | 173 | 182 | 168 | 171 | 164 |
| Jets | 175 | 174 | 188 | 168 | 166 | 174 | 181 | 181 | 170 | 188 | 190 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct stem (16, 17, 18, 19) | B1 | Correct stem, ignore extra values (not in reverse, not split). If a split stem-and-leaf plot is used (i.e., stem values repeated), the remaining B marks are available. |
| Aces: \(9\ 8\ 6\ 4 \mid 16 \mid\); \(4\ 3\ 1 \mid 17 \mid\); \(2\ 2\ 1\ 0 \mid 18 \mid\); \(19 \mid\) — leaves in order right to left | B1 | Correct Aces labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation |
| Jets: \(\mid 16 \mid 6\ 8\); \(\mid 17 \mid 0\ 4\ 4\ 5\); \(\mid 18 \mid 1\ 1\ 8\ 8\); \(\mid 19 \mid 0\) — leaves in order | B1 | Correct Jets labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation |
| Key: \(1 \mid 17 \mid 0\) means 171 cm for the Aces and 170 cm for the Jets | B1 | Correct key for their diagram, need both teams labelled and 'cm' stated at least once here, or in leaf headings or title |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Median \(= 173\) [cm] | B1 | Accept \(Q_2\); must be identified |
| \([\text{IQR} =]\ 181 - 168\) | M1 | \(180 \leqslant UQ \leqslant 182 - 166 \leqslant LQ \leqslant 169\); implied if both quartile values are stated and an appropriate IQR calculated accurately |
| \(13\) [cm] | A1 | www. If M0 scored SC B1 for 13 www |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Jets have a greater variety of heights. Jets have a wider range of height. Jets have a greater/larger/bigger/wider/'more' spread of heights. Aces have a smaller variety of height etc. | B1 | [Jets IQR \(= 18\) cm, Range \(= 24\) cm; Aces IQR \(=\) *their* 4(b), Range \(= 18\) cm]. Comment about spread in context, must include height. Comparison of values does not score until a comment in context is made. If values for range or IQR are stated, they must be correct or FT from 4(b). If more than one comment about spread, mark the final comment. Additional comments about central tendency score B0. |
| 1 |
## Question 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct stem (16, 17, 18, 19) | B1 | Correct stem, ignore extra values (not in reverse, not split). If a split stem-and-leaf plot is used (i.e., stem values repeated), the remaining B marks are available. |
| Aces: $9\ 8\ 6\ 4 \mid 16 \mid$; $4\ 3\ 1 \mid 17 \mid$; $2\ 2\ 1\ 0 \mid 18 \mid$; $19 \mid$ — leaves in order right to left | B1 | Correct Aces labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation |
| Jets: $\mid 16 \mid 6\ 8$; $\mid 17 \mid 0\ 4\ 4\ 5$; $\mid 18 \mid 1\ 1\ 8\ 8$; $\mid 19 \mid 0$ — leaves in order | B1 | Correct Jets labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation |
| Key: $1 \mid 17 \mid 0$ means 171 cm for the Aces and 170 cm for the Jets | B1 | Correct key for their diagram, need both teams labelled and 'cm' stated at least once here, or in leaf headings or title |
| | **4** | |
---
## Question 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Median $= 173$ [cm] | B1 | Accept $Q_2$; must be identified |
| $[\text{IQR} =]\ 181 - 168$ | M1 | $180 \leqslant UQ \leqslant 182 - 166 \leqslant LQ \leqslant 169$; implied if both quartile values are stated and an appropriate IQR calculated accurately |
| $13$ [cm] | A1 | www. If M0 scored **SC B1** for 13 www |
| | **3** | |
---
## Question 4(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Jets have a greater variety of heights. Jets have a wider range of height. Jets have a greater/larger/bigger/wider/'more' spread of heights. Aces have a smaller variety of height etc. | B1 | [Jets IQR $= 18$ cm, Range $= 24$ cm; Aces IQR $=$ *their* **4(b)**, Range $= 18$ cm]. Comment about spread in context, must include height. Comparison of values does not score until a comment in context is made. If values for range or IQR are stated, they must be correct or FT from **4(b)**. If more than one comment about spread, mark the final comment. Additional comments about central tendency score B0. |
| | **1** | |4 The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the following table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Aces & 180 & 174 & 169 & 182 & 181 & 166 & 173 & 182 & 168 & 171 & 164 \\
\hline
Jets & 175 & 174 & 188 & 168 & 166 & 174 & 181 & 181 & 170 & 188 & 190 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a back-to-back stem-and-leaf diagram to represent this information with the Aces on the left-hand side of the diagram.
\item Find the median and the interquartile range of the heights of the players in the Aces.
\item Give one comment comparing the spread of the heights of the Aces with the spread of the heights of the Jets.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2023 Q4 [8]}}