| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate using histogram bar dimensions |
| Difficulty | Standard +0.3 This is a straightforward histogram question testing understanding that frequency density (not frequency) determines the modal class. Part (a) requires recalling a definition, while part (b) involves routine calculations using the relationship between frequency, class width, and frequency density. The arithmetic is simple and the method is standard S1 content, making it slightly easier than average. |
| Spec | 2.02b Histogram: area represents frequency |
| Answer | Marks |
|---|---|
| (a) Frequency density may not be greatest in that class | B2 |
| (b) 1000 families: 50 cm², so 400 families: 20 cm² | M1 |
| Width of '30 - 40' = 2·5 cm, so width of '15 - 20' = 1·25 cm | M1 A1 A1 |
| Area of '15 - 20' = 15 cm², so height = \(15 \div 1.25 = 12\) cm | B1 M1 A1 |
| 9 marks total |
(a) Frequency density may not be greatest in that class | B2 |
(b) 1000 families: 50 cm², so 400 families: 20 cm² | M1 |
Width of '30 - 40' = 2·5 cm, so width of '15 - 20' = 1·25 cm | M1 A1 A1 |
Area of '15 - 20' = 15 cm², so height = $15 \div 1.25 = 12$ cm | B1 M1 A1 |
| 9 marks total |\begin{enumerate}[label=(\alph*)]
\item Explain briefly why, for data grouped in unequal classes, the class with the highest frequency may not be the modal class. [2 marks]
\end{enumerate}
In a histogram drawn to represent the annual incomes (in thousands of pounds) of 1000 families, the modal class was 15 - 20 (i.e. $£x$, where $15000 \leq x < 20000$), with frequency 300. The highest frequency in a class was 400, for the class 30 - 40, and the bar representing this class was 8 cm high. The total area under the histogram was 50 cm$^2$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the height and the width of the bar representing the modal class. [7 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [9]}}