| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Moderate -0.3 This is a straightforward S1 statistics question requiring standard histogram construction with unequal class widths (calculating frequency densities) and finding the interquartile range from grouped data using linear interpolation. Both are routine textbook procedures with no conceptual challenges, making it slightly easier than average. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Height \(( h \mathrm {~cm} )\) | \(130 \leqslant h < 150\) | \(150 \leqslant h < 160\) | \(160 \leqslant h < 170\) | \(170 \leqslant h < 175\) | \(175 \leqslant h < 195\) |
| Frequency | 16 | 32 | 76 | 64 | 12 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| cw: 20, 10, 10, 5, 20; fd: 0.8, 3.2, 7.6, 12.8, 0.6 | M1 | At least four frequency densities calculated \(\frac{f}{cw}\) (e.g. \(\frac{16}{20}\)). Condone \(\frac{f}{cw \pm 0.5}\) if unsimplified. Accept unsimplified, may be read from graph using *their* scale no lower than 1 cm = fd 2. |
| All bar heights correct on graph, not FT | A1 | Using their suitable linear scale with at least three values indicated, no lower than 1 cm = fd 2. |
| Bar ends at 150, 160, 170, 175, 195. Five bars drawn | B1 | Horizontal linear scale no lower than 1 cm = 10 cm, with at least three values indicated, \(130 \leqslant\) horizontal scale \(\leqslant 195\). |
| Axes labelled frequency density (fd) height (h) and cm, OE, or appropriate title | B1 | Axes may be reversed. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([LQ:]\ 160 \leqslant h < 170\ \ [UQ:]\ 170 \leqslant h < 175\) | M1 | \(170 \leqslant h < 175 - 160 \leqslant h < 170\); UQ and LQ classes seen. |
| \(175 - 160 = 15\) | A1 | |
| If M0 scored, SC B1 for \(175 - 160 = 15\). |
## Question 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| cw: 20, 10, 10, 5, 20; fd: 0.8, 3.2, 7.6, 12.8, 0.6 | M1 | At least four frequency densities calculated $\frac{f}{cw}$ (e.g. $\frac{16}{20}$). Condone $\frac{f}{cw \pm 0.5}$ if unsimplified. Accept unsimplified, may be read from graph using *their* scale no lower than 1 cm = fd 2. |
| All bar heights correct on graph, not FT | A1 | Using their suitable linear scale with at least three values indicated, no lower than 1 cm = fd 2. |
| Bar ends at 150, 160, 170, 175, 195. Five bars drawn | B1 | Horizontal linear scale no lower than 1 cm = 10 cm, with at least three values indicated, $130 \leqslant$ horizontal scale $\leqslant 195$. |
| Axes labelled frequency density (fd) height (h) and cm, OE, or appropriate title | B1 | Axes may be reversed. |
## Question 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[LQ:]\ 160 \leqslant h < 170\ \ [UQ:]\ 170 \leqslant h < 175$ | M1 | $170 \leqslant h < 175 - 160 \leqslant h < 170$; UQ and LQ classes seen. |
| $175 - 160 = 15$ | A1 | |
| | | If M0 scored, **SC B1** for $175 - 160 = 15$. |3 The heights, in cm, of 200 adults in Barimba are summarised in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Height $( h \mathrm {~cm} )$ & $130 \leqslant h < 150$ & $150 \leqslant h < 160$ & $160 \leqslant h < 170$ & $170 \leqslant h < 175$ & $175 \leqslant h < 195$ \\
\hline
Frequency & 16 & 32 & 76 & 64 & 12 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a histogram to represent this information.\\
\includegraphics[max width=\textwidth, alt={}, center]{a909cef1-8a22-4cef-b0b7-c48316304c0c-04_1397_1495_762_287}
\item The interquartile range is $R \mathrm {~cm}$. Show that $R$ is not greater than 15 .
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2024 Q3 [6]}}