| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (unequal class widths) |
| Difficulty | Easy -1.8 This is a routine, mechanical task requiring only the ability to calculate cumulative frequencies and plot points on a provided grid. No problem-solving, interpretation, or conceptual understanding beyond basic definitions is needed—significantly easier than typical A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| Time (seconds) | \(3 - 5\) | \(6 - 8\) | \(9 - 11\) | \(12 - 16\) | \(17 - 25\) |
| Frequency | 10 | 15 | 17 | 4 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Points \((5.5, 10)\), \((8.5, 25)\), \((11.5, 42)\), \((16.5, 46)\), \((25.5, 48)\) | B1 | Correct cfs values seen listed, in or by table or on graph, 0 not required |
| Axes and scale | B1 | Axes labelled "cumulative frequency" (or cf) and "time [or t etc.] (in) seconds (or sec etc.)". Linear scales – cf \(0\)–\(48\), time \(2.5\)–\(25.5\) (ignore \(<2.5\) on time). At least 3 values stated on each axis, but \((0,0)\) can be implied without stating. |
| Curve/line segments drawn | B1 | All points plotted accurately; \((5, 10)\) etc. scores B0. Curve or line segments drawn starting at \((5.5, 10)\) and passing within '1 scale unit' vertically and horizontally of plotted points |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(48 - 35 = 13\) | M1 | Subtract 35 (checked \(\pm 1\) mm on graph) from 48 or 50 |
| \(t = 6.5\) sec | A1 | \(6 \leqslant \text{Ans} \leqslant 7\) |
| Total: 2 |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Points $(5.5, 10)$, $(8.5, 25)$, $(11.5, 42)$, $(16.5, 46)$, $(25.5, 48)$ | B1 | Correct cfs values seen listed, in or by table or on graph, 0 not required |
| Axes and scale | B1 | Axes labelled "cumulative frequency" (or cf) and "time [or t etc.] (in) seconds (or sec etc.)". Linear scales – cf $0$–$48$, time $2.5$–$25.5$ (ignore $<2.5$ on time). At least 3 values stated on each axis, but $(0,0)$ can be implied without stating. |
| Curve/line segments drawn | B1 | All points plotted accurately; $(5, 10)$ etc. scores **B0**. Curve or line segments drawn starting at $(5.5, 10)$ and passing within '1 scale unit' vertically and horizontally of plotted points |
| **Total: 3** | | |
---
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $48 - 35 = 13$ | M1 | Subtract 35 (checked $\pm 1$ mm on graph) from 48 or 50 |
| $t = 6.5$ sec | A1 | $6 \leqslant \text{Ans} \leqslant 7$ |
| **Total: 2** | | |
---2 The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summarised in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time (seconds) & $3 - 5$ & $6 - 8$ & $9 - 11$ & $12 - 16$ & $17 - 25$ \\
\hline
Frequency & 10 & 15 & 17 & 4 & 2 \\
\hline
\end{tabular}
\end{center}
(i) On the grid, draw a cumulative frequency graph to represent this information.\\
\includegraphics[max width=\textwidth, alt={}, center]{ee1e5987-315b-48eb-8dba-b9d4d34c87c9-03_1207_1406_897_411}\\
(ii) 35 of these cars accelerated from 0 to 30 metres per second in a time more than $t$ seconds. Estimate the value of $t$.\\
\hfill \mbox{\textit{CAIE S1 2017 Q2 [5]}}