| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| 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 straightforward data handling question requiring basic construction of a stem-and-leaf diagram and calculation of IQR from ordered data. Both tasks are routine recall of standard procedures with no problem-solving or conceptual challenge beyond following learned algorithms. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Lakeview | 10 | 14 | 19 | 22 | 26 | 27 | 28 | 30 | 32 | 33 | 41 |
| Riverside | 23 | 36 | 21 | 18 | 37 | 25 | 18 | 20 | 24 | 30 | 25 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct stem (1, 2, 3, 4) | B1 | Correct stem, ignore extra values |
| Lakeview leaves in order from right to left, lined up vertically, no commas: \(9\ 4\ 0\ \ | 1\), \(8\ 7\ 6\ 2\ \ | 2\), \(3\ 2\ 0\ \ |
| Riverside leaves in order, lined up vertically, no commas: \(\ | 1\ 8\ 8\), \(\ | 2\ 0\ 1\ 3\ 4\ 5\ 5\), \(\ |
| Key: \(6\ | 2\ | 3\) means \(26\)m for Lakeview and \(23\)m for Riverside |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(UQ = 32\), \(LQ = 19\) | M1 | \((30 \leqslant UQ \leqslant 33) - (14 \leqslant LQ \leqslant 22)\) |
| \(IQR = 32 - 19 = 13\) | A1 | WWW |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct stem (1, 2, 3, 4) | B1 | Correct stem, ignore extra values |
| Lakeview leaves in order from right to left, lined up vertically, no commas: $9\ 4\ 0\ \|1$, $8\ 7\ 6\ 2\ \|2$, $3\ 2\ 0\ \|3$, $1\ \|4$ | B1 | Correct Lakeview labelled on left, leaves in order from right to left and lined up vertically, no commas |
| Riverside leaves in order, lined up vertically, no commas: $\|1\ 8\ 8$, $\|2\ 0\ 1\ 3\ 4\ 5\ 5$, $\|3\ 0\ 6\ 7$ | B1 | Correct Riverside labelled on same diagram, leaves in order and lined up vertically, no commas |
| Key: $6\|2\|3$ means $26$m for Lakeview and $23$m for Riverside | B1 | Correct key; both teams identified and 'm' stated at least once. **SC** If 2 separate diagrams drawn: **SC B1** if both keys meet criteria |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $UQ = 32$, $LQ = 19$ | M1 | $(30 \leqslant UQ \leqslant 33) - (14 \leqslant LQ \leqslant 22)$ |
| $IQR = 32 - 19 = 13$ | A1 | WWW |2 Lakeview and Riverside are two schools. The pupils at both schools took part in a competition to see how far they could throw a ball. The distances thrown, to the nearest metre, by 11 pupils from each school are shown in the following table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Lakeview & 10 & 14 & 19 & 22 & 26 & 27 & 28 & 30 & 32 & 33 & 41 \\
\hline
Riverside & 23 & 36 & 21 & 18 & 37 & 25 & 18 & 20 & 24 & 30 & 25 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a back-to-back stem-and-leaf diagram to represent this information, with Lakeview on the left-hand side.
\item Find the interquartile range of the distances thrown by the 11 pupils at Lakeview school.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2021 Q2 [6]}}