| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Use linear interpolation for median or quartiles |
| Difficulty | Moderate -0.3 This is a standard S1 cumulative frequency question requiring routine techniques: naming a graph type, linear interpolation for median/quartiles/percentiles, drawing a box plot, and basic comparison. While multi-part with 15 marks total, each component uses straightforward textbook methods with no novel problem-solving or conceptual challenges beyond standard curriculum expectations. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Selling Price | Number of Houses | Selling Price | Number of Houses |
| Up to £50 000 | 60 | Up to £150 000 | 642 |
| Up to £75 000 | 227 | Up to £200 000 | 805 |
| Up to £100 000 | 305 | Up to £500 000 | 849 |
| Up to £125 000 | 414 | Up to £750 000 | 1000 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Cumulative frequency graph drawn | B1 | |
| (b) \(Q_1 = 75\,000 + \frac{86}{228} \times 25\,000 = £82\,372\) | M1 A1 | |
| \(Q_2 = 125\,000 + \frac{23}{78} \times 25\,000 = £134\,430\) | M1 A1 | |
| \(Q_3 = 150\,000 + \frac{108}{163} \times 50\,000 = £183\,129\) | M1 A1 | |
| (c) \(100\,000 + \frac{65}{109} \times 25\,000 = £114\,908\) | M1 A1 | |
| (d) Box plot drawn; upper limit \(£732\,000\) | B4 | |
| (e) First town IQR = \(£100\,757\). Second town has higher median and smaller IQR, so is more expensive overall and more consistent | B1 B1 | 15 marks total |
(a) Cumulative frequency graph drawn | B1 |
(b) $Q_1 = 75\,000 + \frac{86}{228} \times 25\,000 = £82\,372$ | M1 A1 |
$Q_2 = 125\,000 + \frac{23}{78} \times 25\,000 = £134\,430$ | M1 A1 |
$Q_3 = 150\,000 + \frac{108}{163} \times 50\,000 = £183\,129$ | M1 A1 |
(c) $100\,000 + \frac{65}{109} \times 25\,000 = £114\,908$ | M1 A1 |
(d) Box plot drawn; upper limit $£732\,000$ | B4 |
(e) First town IQR = $£100\,757$. Second town has higher median and smaller IQR, so is more expensive overall and more consistent | B1 B1 | 15 marks total1000 houses were sold in a small town in a one-year period. The selling prices were as given in the following table:
\begin{tabular}{|c|c||c|c|}
\hline
Selling Price & Number of Houses & Selling Price & Number of Houses \\
\hline
Up to £50 000 & 60 & Up to £150 000 & 642 \\
Up to £75 000 & 227 & Up to £200 000 & 805 \\
Up to £100 000 & 305 & Up to £500 000 & 849 \\
Up to £125 000 & 414 & Up to £750 000 & 1000 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Name (do not draw) a suitable type of graph for illustrating this data. [1 mark]
\item Use interpolation to find estimates of the median and the quartiles. [6 marks]
\item Estimate the 37th percentile. [2 marks]
\end{enumerate}
Given further that the lowest price was £42 000 and the range of the prices was £690 000,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item draw a box plot to represent the data. Show your scale clearly. [4 marks]
\end{enumerate}
In another town the median price was £149 000, and the interquartile range was £90 000.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item Briefly compare the prices in the two towns using this information. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [15]}}