| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Direct cumulative frequency graph reading |
| Difficulty | Easy -1.8 This question requires only direct reading of values from a cumulative frequency graph with no calculations or interpretation beyond basic percentile concepts. All three parts involve straightforward graph reading: (a) read y-value at x=100, (b) find x-value at y=104 (65% of 160), (c) find Q3-Q1. This is purely mechanical with no problem-solving element, making it significantly easier than average A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(60\) | B1 | Accept 60 or 61. No decimals |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(65\%\) of \(160 = 104\) | M1 | \(0.65 \times 160\ (=104)\) seen unsimplified or implied by use on graph |
| \(136\) (cm) | A1 | Use of graph must be seen. SCB1 correct value (136 only) if neither 104 nor use of graph are evident |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| UQ: \(150\), LQ: \(76\) | M1 | \(UQ - LQ\); \(148 \leqslant UQ \leqslant 152\); \(74 \leqslant LQ \leqslant 78\) |
| \(IQR = 150 - 76 = 74\) [cm] | A1 | Must be from \(150 - 76\) |
| Total: 2 |
**Question 1:**
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $60$ | B1 | Accept 60 or 61. No decimals |
| | **Total: 1** | |
---
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $65\%$ of $160 = 104$ | M1 | $0.65 \times 160\ (=104)$ seen unsimplified or implied by use on graph |
| $136$ (cm) | A1 | Use of graph must be seen. **SCB1** correct value (136 only) if neither 104 nor use of graph are evident |
| | **Total: 2** | |
---
**Part (c):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| UQ: $150$, LQ: $76$ | M1 | $UQ - LQ$; $148 \leqslant UQ \leqslant 152$; $74 \leqslant LQ \leqslant 78$ |
| $IQR = 150 - 76 = 74$ [cm] | A1 | Must be from $150 - 76$ |
| | **Total: 2** | |1 The heights in cm of 160 sunflower plants were measured. The results are summarised on the following cumulative frequency curve.\\
\includegraphics[max width=\textwidth, alt={}, center]{b72bd3eb-2c10-4d01-ab18-74d6fb812f27-02_1783_1424_404_356}
\begin{enumerate}[label=(\alph*)]
\item Use the graph to estimate the number of plants with heights less than 100 cm .
\item Use the graph to estimate the 65th percentile of the distribution.
\item Use the graph to estimate the interquartile range of the heights of these plants.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2021 Q1 [5]}}