| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2022 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from cumulative frequency table |
| Difficulty | Easy -1.8 This is a straightforward graph-plotting exercise requiring students to plot given cumulative frequency values against time boundaries and draw a smooth curve. It involves no calculation, interpretation, or problem-solving—only the mechanical skill of accurate plotting from a provided table. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| Time taken \(( t\) minutes \()\) | \(t \leqslant 25\) | \(t \leqslant 50\) | \(t \leqslant 75\) | \(t \leqslant 100\) | \(t \leqslant 150\) | \(t \leqslant 200\) |
| Cumulative frequency | 16 | 44 | 86 | 104 | 132 | 150 |
| \multirow{2}{*}{} | |||||||||||||||||
| \multirow{3}{*}}{ | |||||||||||||||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cumulative frequency (cf) graph plotted with at least 3 points accurately at class upper end points \((25,16)\) \((50,44)\) \((75,86)\) \((100,104)\) \((150,132)\) \((200,150)\). Linear cf scale \(0 \leqslant \text{cf} \leqslant 150\) and linear time scale \(0 \leqslant \text{time(mins)} \leqslant 200\) with at least 3 values identified on each axis. | M1 | At least 3 points plotted accurately at class upper end points as listed. Linear cf scale and linear time scale with at least 3 values identified on each axis. |
| All points plotted correctly, curve drawn (within tolerance) and joined to \((0,0)\). Axes labelled cumulative frequency (cf), time (\(t\)) and minutes (min), or a suitable title. | A1 | All points plotted correctly, curve drawn within tolerance and joined to \((0,0)\). Axes labelled cumulative frequency (cf), time (\(t\)) and minutes (min), or a suitable title. |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Line from cumulative frequency \(= 30\) to meet graph at \(t\) is between \(37.5\) and \(42\) | B1 FT | Not from wrong working. Must be an increasing cumulative frequency graph. |
| Total: 1 |
## Question 1:
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cumulative frequency (cf) graph plotted with at least 3 points accurately at class upper end points $(25,16)$ $(50,44)$ $(75,86)$ $(100,104)$ $(150,132)$ $(200,150)$. Linear cf scale $0 \leqslant \text{cf} \leqslant 150$ and linear time scale $0 \leqslant \text{time(mins)} \leqslant 200$ with at least 3 values identified on each axis. | M1 | At least 3 points plotted accurately at class upper end points as listed. Linear cf scale and linear time scale with at least 3 values identified on each axis. |
| All points plotted correctly, curve drawn (within tolerance) and joined to $(0,0)$. Axes labelled cumulative frequency (cf), time ($t$) and minutes (min), or a suitable title. | A1 | All points plotted correctly, curve drawn within tolerance and joined to $(0,0)$. Axes labelled cumulative frequency (cf), time ($t$) and minutes (min), or a suitable title. |
| | **Total: 2** | |
---
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Line from cumulative frequency $= 30$ to meet graph at $t$ is between $37.5$ and $42$ | B1 FT | Not from wrong working. Must be an increasing cumulative frequency graph. |
| | **Total: 1** | |1 The time taken, $t$ minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
Time taken $( t$ minutes $)$ & $t \leqslant 25$ & $t \leqslant 50$ & $t \leqslant 75$ & $t \leqslant 100$ & $t \leqslant 150$ & $t \leqslant 200$ \\
\hline
Cumulative frequency & 16 & 44 & 86 & 104 & 132 & 150 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a cumulative frequency graph to illustrate the data.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
& \multicolumn{17}{|c|}{} \\
\hline
\multicolumn{18}{|c|}{\multirow{2}{*}{}} \\
\hline
\multicolumn{18}{|c|}{\multirow{3}{*}}{} \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
& & & & & & & & & & & & & & & & & \\
\hline
\end{tabular}
\end{center}
\item Use your graph to estimate the 20th percentile of the data.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2022 Q1 [3]}}