| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (equal class widths) |
| Difficulty | Easy -1.8 This is a straightforward, routine statistics question requiring only basic recall of cumulative frequency concepts. Students simply add frequencies cumulatively, plot points, and read off standard percentiles (median, quartiles) from the graph—no problem-solving or conceptual insight needed beyond textbook procedures. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Number of minutes late \(( t )\) | \(- 2 \leqslant t < 0\) | \(0 \leqslant t < 2\) | \(2 \leqslant t < 4\) | \(4 \leqslant t < 6\) | \(6 \leqslant t < 10\) |
| Number of trains | 43 | 51 | 69 | 22 | 19 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Some trains were up to 2 minutes early | B1 [1] | Or sensible equivalent, must use the idea 'early'; 2 not needed |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| CF table: Min late less than: \(0, 2, 4, 6, 10\); CF: \(43, 94, 163, 185, 204\) | M1 | Attempt at CF table with upper limits, no halves |
| Uniform linear scales from at least 0 to 10 and 0 to 204 | M1 | At least one axis labelled, CF or mins or \(t\) |
| Attempt at graph with 5 points; \((-2, 0)\) not necessary | M1 | Could be midpoints or lower bounds (not fd) |
| Attempt at median along 102 or 102.5 line | M1 | |
| Attempt at LQ along 51/52 line and UQ along 153/154 line from graph | M1 | |
| Median \(\approx 2.1\) to \(2.4\) min | B1 | Correct median |
| IQ range \(\approx 3.2\) to \(3.6\) min | A1 [7] | Correct IQ range, allow from midpoints etc |
## Question 5:
**Part (i)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| Some trains were up to 2 minutes early | B1 **[1]** | Or sensible equivalent, must use the idea 'early'; 2 not needed |
**Part (ii)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| CF table: Min late less than: $0, 2, 4, 6, 10$; CF: $43, 94, 163, 185, 204$ | M1 | Attempt at CF table with upper limits, no halves |
| Uniform linear scales from at least 0 to 10 and 0 to 204 | M1 | At least one axis labelled, CF or mins or $t$ |
| Attempt at graph with 5 points; $(-2, 0)$ not necessary | M1 | Could be midpoints or lower bounds (not fd) |
| Attempt at median along 102 or 102.5 line | M1 | |
| Attempt at LQ along 51/52 line and UQ along 153/154 line from graph | M1 | |
| Median $\approx 2.1$ to $2.4$ min | B1 | Correct median |
| IQ range $\approx 3.2$ to $3.6$ min | A1 **[7]** | Correct IQ range, allow from midpoints etc |
---5 The arrival times of 204 trains were noted and the number of minutes, $t$, that each train was late was recorded. The results are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Number of minutes late $( t )$ & $- 2 \leqslant t < 0$ & $0 \leqslant t < 2$ & $2 \leqslant t < 4$ & $4 \leqslant t < 6$ & $6 \leqslant t < 10$ \\
\hline
Number of trains & 43 & 51 & 69 & 22 & 19 \\
\hline
\end{tabular}
\end{center}
(i) Explain what $- 2 \leqslant t < 0$ means about the arrival times of trains.\\
(ii) Draw a cumulative frequency graph, and from it estimate the median and the interquartile range of the number of minutes late of these trains.
\hfill \mbox{\textit{CAIE S1 2007 Q5 [8]}}