| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Direct frequency calculation from histogram |
| Difficulty | Easy -1.2 This is a straightforward histogram interpretation question requiring students to read frequency density values and multiply by class widths to find frequencies. It tests basic understanding of histograms (frequency = frequency density × class width) with no problem-solving or conceptual challenges beyond standard S1 recall. |
| Spec | 2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Width of bar (90.5 – 78.5): frequency density = \(0.5 \times 12\) or 6 | M1, A1 | M1 for correct width; A1 for \(0.5 \times 12\) or 6 |
| Total area \(= (1\times6)+(1\times7)+(4\times2)+\ldots = 70\) | M1, B1 | M1 for area of correct bar \(\times \frac{140}{\text{their } 70}\); B1 for 70 seen anywhere |
| \((90.5 - 78.5) \times \frac{1}{2} \times \frac{140}{\text{their } 70}\) | ||
| Number of runners = 12 | A1 | Beware: \(90.5 - 78.5 = 12\) scores M1A0M0B0A0 |
## Question 3:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Width of bar (90.5 – 78.5): frequency density = $0.5 \times 12$ or 6 | M1, A1 | M1 for correct width; A1 for $0.5 \times 12$ or 6 |
| Total area $= (1\times6)+(1\times7)+(4\times2)+\ldots = 70$ | M1, B1 | M1 for area of correct bar $\times \frac{140}{\text{their } 70}$; B1 for 70 seen anywhere |
| $(90.5 - 78.5) \times \frac{1}{2} \times \frac{140}{\text{their } 70}$ | | |
| Number of runners = **12** | A1 | Beware: $90.5 - 78.5 = 12$ scores M1A0M0B0A0 |
---3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{af84d17b-5308-4b1e-99b5-40c5df5bf01e-06_1027_1509_367_258}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Use the histogram to calculate the number of runners who took between 78.5 and 90.5 minutes to complete the fun run.\\
\hfill \mbox{\textit{Edexcel S1 2008 Q3 [5]}}