| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate frequency density from frequency |
| Difficulty | Easy -1.8 This is a straightforward application of the formula frequency density = frequency ÷ class width. Students only need to identify class widths (accounting for 'correct to nearest minute') and apply basic arithmetic. This is routine recall with minimal problem-solving, making it easier than typical A-level questions. |
| Spec | 2.02b Histogram: area represents frequency |
| Time \(( t\) minutes \()\) | \(60 - 62\) | \(63 - 64\) | \(65 - 67\) | \(68 - 71\) |
| Frequency (number of days) | 3 | 9 | 6 | \(b\) |
| Frequency density | 1 | \(a\) | 2 | 1.5 |
| \includegraphics[max width=\textwidth, alt={}]{34ae4f06-d485-4138-82d8-902b70f08995-04_206_100_1516_441} | " | □ | \(\_\_\_\_\) | □ | □ □ | \includegraphics[max width=\textwidth, alt={}]{34ae4f06-d485-4138-82d8-902b70f08995-04_204_28_1518_1197} | \(\_\_\_\_\) | □ | ||||||||||||||||||||||||||||||||||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(a = 9/\text{cw}\) | M1 | Using \(\text{fd} = f/\text{cw}\) |
| \(= 9/2 = 4.5\) | A1 | Correct \(a\) |
| \(1.5 = b/4\) so \(b = 6\) | A1 | Correct \(b\) |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct heights ft their \(b\) | B1\(\sqrt{}\) | Correct heights ft their \(b\) |
| Correct widths, i.e. 3, 2, 3, 4 starting either 60 or 59.5 | B1 | Correct widths |
| Labels: fd, time or minutes and squiggle and bars from 59.5 to 71.5 | B1 | Labels fd, time or minutes and squiggle and bars from 59.5 to 71.5 |
| Total: 3 |
## Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $a = 9/\text{cw}$ | M1 | Using $\text{fd} = f/\text{cw}$ |
| $= 9/2 = 4.5$ | A1 | Correct $a$ |
| $1.5 = b/4$ so $b = 6$ | A1 | Correct $b$ |
| **Total: 3** | | |
---
## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct heights ft their $b$ | B1$\sqrt{}$ | Correct heights ft their $b$ |
| Correct widths, i.e. 3, 2, 3, 4 starting either 60 or 59.5 | B1 | Correct widths |
| Labels: fd, time or minutes and squiggle and bars from 59.5 to 71.5 | B1 | Labels fd, time or minutes and squiggle and bars from 59.5 to 71.5 |
| **Total: 3** | | |
---3 Robert has a part-time job delivering newspapers. On a number of days he noted the time, correct to the nearest minute, that it took him to do his job. Robert used his results to draw up the following table; two of the values in the table are denoted by $a$ and $b$.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Time $( t$ minutes $)$ & $60 - 62$ & $63 - 64$ & $65 - 67$ & $68 - 71$ \\
\hline
Frequency (number of days) & 3 & 9 & 6 & $b$ \\
\hline
Frequency density & 1 & $a$ & 2 & 1.5 \\
\hline
\end{tabular}
\end{center}
(i) Find the values of $a$ and $b$.\\
(ii) Draw a histogram to represent Robert's times.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
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\hline
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\end{tabular}
\end{center}
\hfill \mbox{\textit{CAIE S1 Q3 [6]}}