| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| 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 grouped data question requiring routine application of linear interpolation for quartiles, drawing a box plot, and basic histogram density calculations. While it has multiple parts and requires careful arithmetic with cumulative frequencies, all techniques are textbook procedures with no novel problem-solving or conceptual insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Length \(( \mathrm { cm } )\) | \(5 - 10\) | \(10 - 20\) | \(20 - 25\) | \(25 - 30\) | \(30 - 40\) | \(40 - 60\) | \(60 - 90\) |
| Frequency | 8 | 16 | 20 | 18 | 20 | 14 | 12 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(Q_1 ≈ 20 + \frac{3}{20} \times 5 = 20.75\) and \(Q_2 ≈ 25 + \frac{10}{18} \times 5 = 27.8\) | M1 A1 M1 A1 | |
| \(Q_3 ≈ 30 + \frac{19}{20} \times 10 = 39.5\) | M1 A1 | |
| (b) Box plot drawn | B4 B1 | |
| (c) Positively skewed | B4 B1 | |
| (d) Frequency densities 1.6, 1.6, 4, 3.6, 2, 0.7, 0.4 with Ratio 1 : 10 | M1 A1 | 13 marks |
(a) $Q_1 ≈ 20 + \frac{3}{20} \times 5 = 20.75$ and $Q_2 ≈ 25 + \frac{10}{18} \times 5 = 27.8$ | M1 A1 M1 A1 |
$Q_3 ≈ 30 + \frac{19}{20} \times 10 = 39.5$ | M1 A1 |
(b) Box plot drawn | B4 B1 |
(c) Positively skewed | B4 B1 |
(d) Frequency densities 1.6, 1.6, 4, 3.6, 2, 0.7, 0.4 with Ratio 1 : 10 | M1 A1 | 13 marks3. The frequency distribution for the lengths of 108 fish in an aquarium is given by the following table. The lengths of the fish ranged from 5 cm to 90 cm .
\begin{center}
\begin{tabular}{ | l | | c | c | c | c | c | c | c | }
\hline
Length $( \mathrm { cm } )$ & $5 - 10$ & $10 - 20$ & $20 - 25$ & $25 - 30$ & $30 - 40$ & $40 - 60$ & $60 - 90$ \\
\hline
Frequency & 8 & 16 & 20 & 18 & 20 & 14 & 12 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate estimates of the three quartiles of the distribution.
\item On graph paper, draw a box and whisker plot of the data.
\item Hence describe the skewness of the distribution.
\item If the data were represented by a histogram, what would be the ratio of the heights of the shortest and highest bars?
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [13]}}