| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate using histogram bar dimensions |
| Difficulty | Moderate -0.8 This is a straightforward histogram question testing the fundamental principle that area represents frequency. Students need to apply the formula (frequency density = frequency/class width) twice in routine calculations with no conceptual challenges or multi-step reasoning required. |
| Spec | 2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | M1 | f.d. of 30-34 = \(\frac{33}{5} = 6.4\); \(6.4 \to 19.2\) cm \(\therefore 1 \to 3\) cm |
| M1 A1 | f.d. of 35-39 = \(\frac{28}{5} = 5.6\); \(\therefore\) height = \(3 \times 5.6 = 16.8\) cm | |
| (b) | M1 | height 2.7 cm \(\therefore\) f.d. = \(\frac{2.7}{3} = 0.9\) |
| M1 A1, (6) | \(\therefore \frac{30}{n} = 0.9\); \(n = 18\) |
(a) | M1 | f.d. of 30-34 = $\frac{33}{5} = 6.4$; $6.4 \to 19.2$ cm $\therefore 1 \to 3$ cm
| M1 A1 | f.d. of 35-39 = $\frac{28}{5} = 5.6$; $\therefore$ height = $3 \times 5.6 = 16.8$ cm
(b) | M1 | height 2.7 cm $\therefore$ f.d. = $\frac{2.7}{3} = 0.9$
| M1 A1, (6) | $\therefore \frac{30}{n} = 0.9$; $n = 18$
---A histogram was drawn to show the distribution of age in completed years of the participants on an outward-bound course.
There were 32 people aged 30-34 years on the course. The height of the rectangle representing this group was 19.2 cm and it was 1 cm in width.
Given that there were 28 people aged 35-39 years,
\begin{enumerate}[label=(\alph*)]
\item find the height of the rectangle representing this group. [3 marks]
\end{enumerate}
Given that the height of the rectangle representing people aged 40-59 years was 2.7 cm,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the number of people on the course in this age group. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [6]}}