| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (unequal class widths) |
| Difficulty | Easy -1.2 This is a straightforward application of standard S1 techniques: constructing a cumulative frequency table from grouped data, plotting the cumulative frequency curve, and reading off median and quartiles. It requires only routine procedural knowledge with no problem-solving or conceptual challenges beyond basic interpretation of grouped data. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Time (\(t\) minutes) | \(0 < t \leq 15\) | \(15 < t \leq 30\) | \(30 < t \leq 60\) | \(60 < t \leq 90\) | \(90 < t \leq 120\) |
| Number of meetings | 4 | 7 | 24 | 38 | 7 |
| Answer | Marks | Guidance |
|---|---|---|
| both axes correct | B1 | For correct scales and labels on at least one axis |
| points | M1, A1 | For points at upper bounds or 15.5 or 14.5; All correct and smooth curve or straight lines |
| median, IQ range | B1ft, M1 | On mid-points or upper bounds; For evaluating their UQ – their LQ |
| A1ft 6 | For correct answer, ft on correct upper bounds only |
**both axes correct** | B1 | For correct scales and labels on at least one axis
**points** | M1, A1 | For points at upper bounds or 15.5 or 14.5; All correct and smooth curve or straight lines
**median, IQ range** | B1ft, M1 | On mid-points or upper bounds; For evaluating their UQ – their LQ
| A1ft 6 | For correct answer, ft on correct upper bounds onlyThe manager of a company noted the times spent in 80 meetings. The results were as follows.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Time ($t$ minutes) & $0 < t \leq 15$ & $15 < t \leq 30$ & $30 < t \leq 60$ & $60 < t \leq 90$ & $90 < t \leq 120$ \\
\hline
Number of meetings & 4 & 7 & 24 & 38 & 7 \\
\hline
\end{tabular}
\end{center}
Draw a cumulative frequency graph and use this to estimate the median time and the interquartile range. [6]
\hfill \mbox{\textit{CAIE S1 2002 Q2 [6]}}