| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2022 |
| Session | March |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring standard histogram construction with unequal class widths (calculating frequency densities), identifying the median class by counting to n/2, and recognizing skewness. All parts are routine S1 techniques with no problem-solving or novel insight required, making it easier than average A-level maths. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency |
| Time taken, in minutes | \(1 - 30\) | \(31 - 45\) | \(46 - 65\) | \(66 - 75\) | \(76 - 100\) |
| Frequency | 21 | 30 | 68 | 86 | 45 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Class Width: 30, 15, 20, 10, 25; Frequency Density: 0.7, 2, 3.4, 8.6, 1.8 | M1 | At least 4 frequency densities calculated |
| (all heights correct on graph) | A1 | All heights correct on graph |
| Bar ends at 0.5, 30.5, 45.5, 65.5, 75.5, 100.5 (at axis), 5 bars drawn, condone 0 in first bar, \(0.5 \leqslant\) time axis \(\leqslant 100.5\), linear scale with at least 3 values indicated | B1 | Bar ends at 0.5, 30.5, 45.5, 65.5, 75.5, 100.5 |
| Axes labelled: Frequency density (fd), time (t) and mins (or appropriate title). Linear fd scale, with at least 3 values indicated \(0 \leqslant\) fd axis \(\leqslant 8.6\) | B1 | Axes labelled appropriately |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(66 - 75\) | B1 | Condone \(65.5 - 75.5\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Distribution is not symmetrical | B1 | Or skewed, ignore nature of skew |
## Question 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Class Width: 30, 15, 20, 10, 25; Frequency Density: 0.7, 2, 3.4, 8.6, 1.8 | M1 | At least 4 frequency densities calculated |
| (all heights correct on graph) | A1 | All heights correct on graph |
| Bar ends at 0.5, 30.5, 45.5, 65.5, 75.5, 100.5 (at axis), 5 bars drawn, condone 0 in first bar, $0.5 \leqslant$ time axis $\leqslant 100.5$, linear scale with at least 3 values indicated | B1 | Bar ends at 0.5, 30.5, 45.5, 65.5, 75.5, 100.5 |
| Axes labelled: Frequency density (fd), time (t) and mins (or appropriate title). Linear fd scale, with at least 3 values indicated $0 \leqslant$ fd axis $\leqslant 8.6$ | B1 | Axes labelled appropriately |
## Question 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $66 - 75$ | B1 | Condone $65.5 - 75.5$ |
## Question 3(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Distribution is not symmetrical | B1 | Or skewed, ignore nature of skew |3 At a summer camp an arithmetic test is taken by 250 children. The times taken, to the nearest minute, to complete the test were recorded. The results are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time taken, in minutes & $1 - 30$ & $31 - 45$ & $46 - 65$ & $66 - 75$ & $76 - 100$ \\
\hline
Frequency & 21 & 30 & 68 & 86 & 45 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a histogram to represent this information.\\
\includegraphics[max width=\textwidth, alt={}, center]{c1bc5ac2-6b0e-48c7-92e9-9b8b56b57d90-05_1000_1198_785_516}
\item State which class interval contains the median.
\item Given that an estimate of the mean time is 61.05 minutes, state what feature of the distribution accounts for the median and the mean being different.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2022 Q3 [6]}}