| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Complete frequency table and histogram together |
| Difficulty | Moderate -0.8 This is a standard AS-level statistics question testing histogram interpretation and frequency density calculations. Students must complete missing frequencies using the relationship between bar heights and class widths, then calculate a percentage using linear interpolation. While it requires careful attention to frequency density and class boundaries, it follows a routine procedure with no novel problem-solving required. |
| Spec | 2.02b Histogram: area represents frequency |
| Delay (minutes) | Number of motorists |
| 4-6 | 6 |
| 7-8 | |
| 9 | 17 |
| 10-12 | 45 |
| 13-15 | 9 |
| 16-20 |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | For a fully correct expression for the number of motorists in the interval | AO 2.2a |
| M1 | For clear use of frequency density in (4–6) or (13–15) cases to establish the fd scale. Then use of area to find frequency in one of the missing cases | AO 3.1a |
| A1 | For both correct values seen | AO 1.1b |
| M1 | For realising that total is required and attempting a correct expression for \(\%\) | AO 3.1b |
| A1 | For awrt 67.7\(\%\) | AO 1.1b |
Question 2:
**M1** | For a fully correct expression for the number of motorists in the interval | AO 2.2a
**M1** | For clear use of frequency density in (4–6) or (13–15) cases to establish the fd scale. Then use of area to find frequency in one of the missing cases | AO 3.1a
**A1** | For both correct values seen | AO 1.1b
**M1** | For realising that total is required and attempting a correct expression for $\%$ | AO 3.1b
**A1** | For awrt 67.7$\%$ | AO 1.1b
(5 marks)\begin{enumerate}
\item The partially completed histogram and the partially completed table show the time, to the nearest minute, that a random sample of motorists was delayed by roadworks on a stretch of motorway.\\
\includegraphics[max width=\textwidth, alt={}, center]{8f3dbcb4-3260-4493-a230-12577b4ed691-04_1227_1465_354_301}
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|}
\hline
Delay (minutes) & Number of motorists \\
\hline
4-6 & 6 \\
\hline
7-8 & \\
\hline
9 & 17 \\
\hline
10-12 & 45 \\
\hline
13-15 & 9 \\
\hline
16-20 & \\
\hline
\end{tabular}
\end{center}
Estimate the percentage of these motorists who were delayed by the roadworks for between 8.5 and 13.5 minutes.
\hfill \mbox{\textit{Edexcel AS Paper 2 Q2 [5]}}