| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Moderate -0.3 This is a multi-part statistics question requiring histogram construction with unequal class widths (requiring frequency density calculation), identifying the median class interval (straightforward counting to n/2), and finding the maximum IQR (requires understanding that extreme values within classes maximize the range). While it tests multiple concepts, each step follows standard S1 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.02b Histogram: area represents frequency |
| Population | \(100 - 800\) | \(900 - 1200\) | \(1300 - 2000\) | \(2100 - 3200\) | \(3300 - 4800\) |
| Number of villages | 8 | 12 | 50 | 48 | 32 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| cw: 800, 400, 800, 1200, 1600; fd: 0.01, 0.03, 0.0625, 0.04, 0.02 | M1 | At least 4 frequency densities calculated (F/cw, e.g. \(\frac{8}{800}\), condone \(\frac{8}{n}\), \(799 \leq n \leq 801\)). Accept unsimplified, may be read from graph using *their* scale |
| All heights correct on graph | A1 | |
| Bar ends at 50, 850, 1250, 2050, 3250, 4850 read at axis with horizontal linear scale with at least 3 values indicated. \(50 \leq\) horizontal scale \(\leq 4850\) | B1 | |
| Axes labelled frequency density (fd) and population (pop) OE, or in a title. Linear vertical scale, with at least 3 values indicated. Vertical axis must cover at least range \(0 \leq\) vertical axis \(\leq 0.0625\). Axes may be reversed | B1 | |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2100 - 3200\) | B1 | Accept \(2050 - 3250\) OE. Condone '4th interval' |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(3249 - 1250\) | M1 | \(2050 \leq \text{UQ} \leq 3250 - 1250 \leq \text{LQ} \leq 2050\) |
| \(1999\) | A1 | Condone \(3250 - 1250 = 2000\) |
| 2 |
## Question 5(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| cw: 800, 400, 800, 1200, 1600; fd: 0.01, 0.03, 0.0625, 0.04, 0.02 | M1 | At least 4 frequency densities calculated (F/cw, e.g. $\frac{8}{800}$, condone $\frac{8}{n}$, $799 \leq n \leq 801$). Accept unsimplified, may be read from graph using *their* scale |
| All heights correct on graph | A1 | |
| Bar ends at 50, 850, 1250, 2050, 3250, 4850 read at axis with horizontal linear scale with at least 3 values indicated. $50 \leq$ horizontal scale $\leq 4850$ | B1 | |
| Axes labelled frequency density (fd) and population (pop) OE, or in a title. Linear vertical scale, with at least 3 values indicated. Vertical axis must cover at least range $0 \leq$ vertical axis $\leq 0.0625$. Axes may be reversed | B1 | |
| | **4** | |
## Question 5(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2100 - 3200$ | B1 | Accept $2050 - 3250$ OE. Condone '4th interval' |
| | **1** | |
## Question 5(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $3249 - 1250$ | M1 | $2050 \leq \text{UQ} \leq 3250 - 1250 \leq \text{LQ} \leq 2050$ |
| $1999$ | A1 | Condone $3250 - 1250 = 2000$ |
| | **2** | |
---5 The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Population & $100 - 800$ & $900 - 1200$ & $1300 - 2000$ & $2100 - 3200$ & $3300 - 4800$ \\
\hline
Number of villages & 8 & 12 & 50 & 48 & 32 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a histogram to represent this information.\\
\includegraphics[max width=\textwidth, alt={}, center]{a7157882-d87e-4efb-abc5-9c9f58197012-08_1395_1195_1043_516}
\item Write down the class interval which contains the median for this information.
\item Find the greatest possible value of the interquartile range for the populations of the 150 villages.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2023 Q5 [7]}}