| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Total sample size from histogram |
| Difficulty | Moderate -0.8 This is a straightforward histogram question requiring understanding that frequency = frequency density × class width, then using proportional reasoning with areas. The calculation is direct: if one bar has area 1.5×12=18 cm² representing 20 people, then 94.5 cm² represents (20/18)×94.5=105 people. This tests basic histogram interpretation with minimal steps, making it easier than average. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(1.5 \times 12 = 18\); 20 people represented by 18 cm² or 1 person represented by 0.9 cm² | M1 | Attempt to relate area to frequency (e.g. \(\frac{20}{18}\) or \(\frac{18}{20}\) seen) |
| \(x = \frac{20 \times 94.5}{18}\) oe | M1 | Correct expression/equation for total frequency e.g. \(\frac{18}{20} = \frac{94.5}{x}\) |
| \(= 105\) (people) | A1 cao | For 105 cao |
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $1.5 \times 12 = 18$; 20 people represented by 18 cm² or 1 person represented by 0.9 cm² | M1 | Attempt to relate area to frequency (e.g. $\frac{20}{18}$ or $\frac{18}{20}$ seen) |
| $x = \frac{20 \times 94.5}{18}$ oe | M1 | Correct expression/equation for total frequency e.g. $\frac{18}{20} = \frac{94.5}{x}$ |
| $= 105$ (people) | A1 cao | For 105 cao |
---\begin{enumerate}
\item The time taken to complete a puzzle, in minutes, is recorded for each person in a club. The times are summarised in a grouped frequency distribution and represented by a histogram.
\end{enumerate}
One of the class intervals has a frequency of 20 and is shown by a bar of width 1.5 cm and height 12 cm on the histogram. The total area under the histogram is $94.5 \mathrm {~cm} ^ { 2 }$
Find the number of people in the club.\\
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\hfill \mbox{\textit{Edexcel S1 2018 Q2 [3]}}