| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from raw data |
| Difficulty | Easy -1.3 This is a straightforward data representation question requiring only mechanical procedures: ordering data, finding five-number summary (min, Q1, median, Q3, max), and drawing standard diagrams. No problem-solving, interpretation, or conceptual understanding is needed—just routine application of basic statistical techniques taught early in S1. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| 23 | 19 | 32 | 14 | 25 |
| 22 | 26 | 36 | 45 | 42 |
| 47 | 28 | 17 | 38 | 15 |
| 46 | 18 | 26 | 22 | 41 |
| 19 | 21 | 28 | 24 | 30 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Stem | leaf | B1 |
| 1 | 4 5 7 8 9 9 | |
| 2 | 1 2 2 3 4 5 6 6 8 8 | B1 |
| 3 | 0 2 6 8 | |
| 4 | 1 2 5 6 7 | |
| Key | 1 | 4 represents 14 glasses (of water) |
| (ii) \(LQ = 20\), Med \(= 26\), \(UQ = 37\) | B1 | Correct median |
| B1 | Correct quartiles | |
| B1√ | Correct on diagram ft any wrong med or quartiles. Linear scale based upon 3 quartiles plotted | |
| Correct end points of attached whiskers not through box | ||
| B1 | ||
| B1 5 | Linear axis, label, both must be seen | |
| SC No values stated | B2 | |
| 3 quartiles on diagram in correct relative positions | ||
| End points of attached whiskers not through box correct relative to quartiles | B1 |
**(i)** Stem | leaf | B1 | Correct stem (or reversed order)
1 | 4 5 7 8 9 9 |
2 | 1 2 2 3 4 5 6 6 8 8 | B1 | Correct leaves, ordered in numerical sequence, with ½ 'column' tolerance
3 | 0 2 6 8 |
4 | 1 2 5 6 7 |
Key |1|4 represents 14 glasses (of water) | B1 3 | Key must include 'glasses' or similar drinking item
**(ii)** $LQ = 20$, Med $= 26$, $UQ = 37$ | B1 | Correct median
| B1 | Correct quartiles
| B1√ | Correct on diagram ft any wrong med or quartiles. Linear scale based upon 3 quartiles plotted
| | Correct end points of attached whiskers not through box
| B1 |
| B1 5 | Linear axis, label, both must be seen
SC No values stated | B2 |
3 quartiles on diagram in correct relative positions |
End points of attached whiskers not through box correct relative to quartiles | B1 |4 A random sample of 25 people recorded the number of glasses of water they drank in a particular week. The results are shown below.
\begin{center}
\begin{tabular}{ l l l l l }
23 & 19 & 32 & 14 & 25 \\
22 & 26 & 36 & 45 & 42 \\
47 & 28 & 17 & 38 & 15 \\
46 & 18 & 26 & 22 & 41 \\
19 & 21 & 28 & 24 & 30 \\
\end{tabular}
\end{center}
(i) Draw a stem-and-leaf diagram to represent the data.\\
(ii) On graph paper draw a box-and-whisker plot to represent the data.
\hfill \mbox{\textit{CAIE S1 2014 Q4 [8]}}