| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Complete frequency table from histogram only |
| Difficulty | Easy -1.2 This is a straightforward histogram interpretation question requiring students to use the relationship frequency = class width × frequency density. The calculations are simple arithmetic with no conceptual challenges beyond understanding this basic formula, making it easier than average for A-level. |
| Spec | 2.02b Histogram: area represents frequency |
| Delay (minutes) | Number of motorists |
| 4-6 | 6 |
| 7-8 | |
| 9 | 21 |
| 10-12 | 45 |
| 13-15 | 9 |
| 16-20 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(14, 5\) | M1 A1 | M1 for \(2×7\) or \(14\) or \(5×1\) or \(5\); A1 for both \(14\) and \(5\) |
| (2 marks) | ||
| (b) \(21 + 45 + 3 = 69\) | M1 A1 | M1 for \(21+45+(0<\text{frequency}<9)\); A1 for \(69\) only. If \(69\) with no working, award M1A1. Incorrect answer with no working M0A0. |
| (2 marks) |
**(a)** $14, 5$ | M1 A1 | M1 for $2×7$ or $14$ or $5×1$ or $5$; A1 for both $14$ and $5$
| | (2 marks) |
**(b)** $21 + 45 + 3 = 69$ | M1 A1 | M1 for $21+45+(0<\text{frequency}<9)$; A1 for $69$ only. If $69$ with no working, award M1A1. Incorrect answer with no working M0A0.
| | (2 marks) |
**Total: 4 marks**
---\begin{enumerate}
\item The histogram in Figure 1 shows the time, to the nearest minute, that a random sample of 100 motorists were delayed by roadworks on a stretch of motorway.
\end{enumerate}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{bc8ef6c7-a321-4ecf-962d-f469a95fc8c8-02_1312_673_349_639}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
(a) Complete the table.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Delay (minutes) & Number of motorists \\
\hline
4-6 & 6 \\
\hline
7-8 & \\
\hline
9 & 21 \\
\hline
10-12 & 45 \\
\hline
13-15 & 9 \\
\hline
16-20 & \\
\hline
\end{tabular}
\end{center}
(b) Estimate the number of motorists who were delayed between 8.5 and 13.5 minutes by the roadworks.
\hfill \mbox{\textit{Edexcel S1 2012 Q1 [4]}}