| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Total sample size from histogram |
| Difficulty | Easy -1.2 This is a straightforward histogram question testing basic understanding that area represents frequency. Part (c) is a simple calculation (3.6×2÷9=0.8), and part (d) requires only division (24÷0.8=30). The conceptual parts (a) and (b) are standard recall. No problem-solving or novel insight required—purely mechanical application of histogram principles. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Time is a continuous variable or data is in a grouped frequency table | B1 | (1 mark) |
| (b) Area is proportional to frequency or \(A \propto f\) or \(A = kf\) | B1 | (1 mark) |
| (c) \(3.6 \times 2 = 0.8 \times 9\) | M1, dM1, A1 cso | 1 child represented by 0.8 |
| (d) \((\text{Total}) = \frac{24}{0.8} = \mathbf{30}\) | M1, A1 | (2 marks) |
**(a)** Time is a continuous variable or data is in a grouped frequency table | B1 | (1 mark)
**(b)** Area is proportional to frequency or $A \propto f$ or $A = kf$ | B1 | (1 mark)
**(c)** $3.6 \times 2 = 0.8 \times 9$ | M1, dM1, A1 cso | 1 child represented by 0.8 | (3 marks)
**(d)** $(\text{Total}) = \frac{24}{0.8} = \mathbf{30}$ | M1, A1 | (2 marks)
**Total: 7 marks**
---\begin{enumerate}
\item A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample. The times were summarised in a grouped frequency table and represented by a histogram.
\end{enumerate}
One of the classes in the grouped frequency distribution was 20-29 and its associated frequency was 9. On the histogram the height of the rectangle representing that class was 3.6 cm and the width was 2 cm .\\
(a) Give a reason to support the use of a histogram to represent these data.\\
(b) Write down the underlying feature associated with each of the bars in a histogram.\\
(c) Show that on this histogram each child was represented by $0.8 \mathrm {~cm} ^ { 2 }$.
The total area under the histogram was $24 \mathrm {~cm} ^ { 2 }$.\\
(d) Find the total number of children in the group.\\
\hfill \mbox{\textit{Edexcel S1 2007 Q5 [7]}}