| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw back-to-back stem-and-leaf diagram |
| Difficulty | Easy -1.3 Part (i) is a straightforward data representation task requiring only careful organization of given data into a standard diagram format. Part (ii) involves basic mean calculation with one unknown—a routine algebraic manipulation. Both parts are mechanical with no problem-solving or conceptual depth required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02g Calculate mean and standard deviation |
| 9-year-olds: | 13.0 | 16.1 | 16.0 | 14.4 | 15.9 | 15.1 | 14.2 | 13.7 | 16.7 | 16.4 | 15.0 | 13.2 |
| 16-year-olds: | 14.8 | 13.0 | 11.4 | 11.7 | 16.5 | 13.7 | 12.8 | 12.9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Stem-and-leaf diagram with stems 11–16, 16 yr olds: 7,4 \ | 11; 9,8 \ | 12; 7,0 \ |
| B1 | One leaf column correct, ordering not necessary | |
| B1 | Other leaf column correct (ordering not nec) and both leaves labelled correctly (could be in key) | |
| Key: \(7\ | 13\ | 2\) means 13.7 minutes and 13.2 minutes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\sum\) (8 pupils) \(= 106.8\) | B1 | 106.8 seen or implied |
| \(\sum\) (9 pupils) \(= 13.6 \times 9\ (= 122.4)\) | B1 | for \(13.6 \times 9\) |
| New pupil's time \(= 15.6\) min | B1ft 3 | Ft on \(122.4 - \text{their } \sum 8\) |
## Question 4:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Stem-and-leaf diagram with stems 11–16, 16 yr olds: 7,4 \| 11; 9,8 \| 12; 7,0 \| 13; 8 \| 14; — \| 15; 5 \| 16; 9 yr olds: 0,2,7 \| 13; 2,4 \| 14; 0,1,9 \| 15; 0,1,4,7 \| 16 | B1 | 3 columns including an integer stem in the middle, single digits in leaves. Can go downwards |
| | B1 | One leaf column correct, ordering not necessary |
| | B1 | Other leaf column correct (ordering not nec) and both leaves labelled correctly (could be in key) |
| Key: $7\|13\|2$ means 13.7 minutes and 13.2 minutes | B1 **4** | Key correct both ways or two keys one each way, must have minutes |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\sum$ (8 pupils) $= 106.8$ | B1 | 106.8 seen or implied |
| $\sum$ (9 pupils) $= 13.6 \times 9\ (= 122.4)$ | B1 | for $13.6 \times 9$ |
| New pupil's time $= 15.6$ min | B1ft **3** | Ft on $122.4 - \text{their } \sum 8$ |
---4 The lengths of time in minutes to swim a certain distance by the members of a class of twelve 9 -year-olds and by the members of a class of eight 16 -year-olds are shown below.
\begin{center}
\begin{tabular}{ r l l l l l l l l l l l l }
9-year-olds: & 13.0 & 16.1 & 16.0 & 14.4 & 15.9 & 15.1 & 14.2 & 13.7 & 16.7 & 16.4 & 15.0 & 13.2 \\
16-year-olds: & 14.8 & 13.0 & 11.4 & 11.7 & 16.5 & 13.7 & 12.8 & 12.9 & & & & \\
\end{tabular}
\end{center}
(i) Draw a back-to-back stem-and-leaf diagram to represent the information above.\\
(ii) A new pupil joined the 16 -year-old class and swam the distance. The mean time for the class of nine pupils was now 13.6 minutes. Find the new pupil's time to swim the distance.
\hfill \mbox{\textit{CAIE S1 2007 Q4 [7]}}