| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2023 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Direct cumulative frequency graph reading |
| Difficulty | Easy -1.8 This is a straightforward cumulative frequency graph reading exercise requiring only direct reading of values at specified cumulative frequencies (Q1 at 30, Q3 at 90, and 65% at 78 for part b). No calculations beyond subtraction for IQR, no interpretation challenges, purely mechanical graph reading with clearly marked scales. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([\text{IQR} =]\ 31 - 23.7\) | M1 | \(30.5 < \text{UQ} < 31.25 - 23.25 < \text{LQ} \leqslant 24\); Evidence of graph use must be seen at least once. |
| \(7.3\) | A1 | \(7.0 \leqslant \text{IQR} \leqslant 7.5\); If M0 scored, SC B1 for \(7.0 \leqslant \text{IQR} \leqslant 7.5\) www. |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([65\%\ \text{of}\ 120 =]\ 78\) | B1 | Seen or implied by use on graph. |
| \(28.5\) | B1 | \(28 < \text{ans} < 29\) |
| Total: 2 |
**Question 1:**
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[\text{IQR} =]\ 31 - 23.7$ | M1 | $30.5 < \text{UQ} < 31.25 - 23.25 < \text{LQ} \leqslant 24$; Evidence of graph use must be seen at least once. |
| $7.3$ | A1 | $7.0 \leqslant \text{IQR} \leqslant 7.5$; If M0 scored, **SC B1** for $7.0 \leqslant \text{IQR} \leqslant 7.5$ www. |
| | **Total: 2** | |
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[65\%\ \text{of}\ 120 =]\ 78$ | B1 | Seen or implied by use on graph. |
| $28.5$ | B1 | $28 < \text{ans} < 29$ |
| | **Total: 2** | |
---1\\
\includegraphics[max width=\textwidth, alt={}, center]{e8c2b51e-d788-4917-829e-1b056a24f520-03_1372_1194_260_479}
The times taken by 120 children to complete a particular puzzle are represented in the cumulative frequency graph.
\begin{enumerate}[label=(\alph*)]
\item Use the graph to estimate the interquartile range of the data.\\
35\% of the children took longer than $T$ seconds to complete the puzzle.
\item Use the graph to estimate the value of $T$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2023 Q1 [4]}}