| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Data representation |
| Type | Direct frequency calculation from histogram |
| Difficulty | Easy -1.2 This is a straightforward histogram question requiring only the fundamental principle that frequency = frequency density × class width. Part (a) involves a simple proportion calculation using the given frequency, while part (b) requires splitting intervals but uses the same basic formula. No complex reasoning or novel insight needed—purely mechanical application of a standard technique taught early in statistics. |
| Spec | 2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| \(30\times2\times1.6/6\) or \(30\times2\times8/30\) oe | M1 (1.1) | or \(15\times80/150\) oe |
| \(= 16\) | A1 (1.1) | Correct answer without working or unclear working: allow M1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Freq \(4\)-\(5 = 24\) or freq \(5\)-\(6 = 12\) | B1 (3.1a) | or freq \(5\)-\(9 = 48\); OR similar with frequency density |
| \(\frac{1}{2}(\text{freq } 4\text{-}5 + \text{freq } 5\text{-}6)\) or \(\frac{1}{2}\times24 + \frac{1}{2}\times12\) | M1 (1.1) | or \(\frac{1}{2}(\text{freq } 4\text{-}5) + \frac{1}{8}(\text{freq } 5\text{-}9)\) oe |
| \(= 18\) | A1 (1.1) | Correct answer without working or unclear working: allow B1M1A1 |
# Question 8(a):
$30\times2\times1.6/6$ or $30\times2\times8/30$ oe | M1 (1.1) | or $15\times80/150$ oe
$= 16$ | A1 (1.1) | Correct answer without working or unclear working: allow M1A1
---
# Question 8(b):
Freq $4$-$5 = 24$ or freq $5$-$6 = 12$ | B1 (3.1a) | or freq $5$-$9 = 48$; OR similar with frequency density
$\frac{1}{2}(\text{freq } 4\text{-}5 + \text{freq } 5\text{-}6)$ or $\frac{1}{2}\times24 + \frac{1}{2}\times12$ | M1 (1.1) | or $\frac{1}{2}(\text{freq } 4\text{-}5) + \frac{1}{8}(\text{freq } 5\text{-}9)$ oe
$= 18$ | A1 (1.1) | Correct answer without working or unclear working: allow B1M1A1
---8 The histogram shows information about the lengths, $l$ centimetres, of a sample of worms of a certain species.\\
\includegraphics[max width=\textwidth, alt={}, center]{4c6b7c92-2fc9-4d4f-a199-8e70f34e5eed-5_904_1284_488_242}
The number of worms in the sample with lengths in the class $3 \leqslant l < 4$ is 30 .
\begin{enumerate}[label=(\alph*)]
\item Find the number of worms in the sample with lengths in the class $0 \leqslant l < 2$.
\item Find an estimate of the number of worms in the sample with lengths in the range $4.5 \leqslant l < 5.5$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q8 [5]}}