| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Cumulative frequency graph construction then interpretation |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring basic cumulative frequency interpretation, histogram construction, and mean estimation from grouped data. All techniques are standard S1 procedures with no problem-solving insight needed—simpler than average A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Journey time (minutes) | \(\leqslant 10\) | \(\leqslant 25\) | \(\leqslant 45\) | \(\leqslant 60\) | \(\leqslant 80\) |
| Cumulative frequency | 0 | 18 | 50 | 59 | 63 |
| Answer | Marks |
|---|---|
| \(32\) | B1 (1) |
| Answer | Marks | Guidance |
|---|---|---|
| freqs | 0 | 18 |
| fd | 0 | 1.2 |
| [Histogram with correct heights] | M1 | Attempt at fd or scaled freq (at least 3 f/cw attempt) |
| Correct heights seen on diagram | A1 | |
| Correct bar ends | B1 | |
| Labels fd and time (mins) and linear axes or squiggle | B1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{17.5 \times 18 + 35 \times 32 + 52.5 \times 9 + 70 \times 4}{63} = \frac{2187.5}{63} = 34.7\) | M1, A1 (2) | \(\Sigma fx/63\) where \(x\) is midpoint attempt not end pt or cw; correct answer |
## Question 4:
**(i)**
$32$ | B1 (1) |
**(ii)**
| freqs | 0 | 18 | 32 | 9 | 4 |
|-------|---|----|----|---|---|
| fd | 0 | 1.2 | 1.6 | 0.6 | 0.2 |
[Histogram with correct heights] | M1 | Attempt at fd or scaled freq (at least 3 f/cw attempt)
Correct heights seen on diagram | A1 |
Correct bar ends | B1 |
Labels fd and time (mins) and linear axes or squiggle | B1 (4) |
**(iii)**
$\frac{17.5 \times 18 + 35 \times 32 + 52.5 \times 9 + 70 \times 4}{63} = \frac{2187.5}{63} = 34.7$ | M1, A1 (2) | $\Sigma fx/63$ where $x$ is midpoint attempt not end pt or cw; correct answer
---4 A survey was made of the journey times of 63 people who cycle to work in a certain town. The results are summarised in the following cumulative frequency table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Journey time (minutes) & $\leqslant 10$ & $\leqslant 25$ & $\leqslant 45$ & $\leqslant 60$ & $\leqslant 80$ \\
\hline
Cumulative frequency & 0 & 18 & 50 & 59 & 63 \\
\hline
\end{tabular}
\end{center}
(i) State how many journey times were between 25 and 45 minutes.\\
(ii) Draw a histogram on graph paper to represent the data.\\
(iii) Calculate an estimate of the mean journey time.
\hfill \mbox{\textit{CAIE S1 2016 Q4 [7]}}