| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from raw data |
| Difficulty | Moderate -0.8 This is a routine S1 data representation question requiring standard procedures: constructing a stem-and-leaf diagram (mechanical sorting), finding quartiles from ordered data (straightforward calculation), and drawing a box plot. While time-consuming with 60 data points, it requires no problem-solving or conceptual insight—just careful execution of textbook methods. The 8 marks for part (a) reflect the tedious nature rather than difficulty. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 17 | 12 | 9 | 23 | 40 | 32 | 11 | 5 | 34 | 22 | 31 | 8 |
| 15 | 45 | 10 | 52 | 14 | 13 | 29 | 43 | 69 | 30 | 15 | 47 |
| 35 | 6 | 24 | 13 | 19 | 26 | 9 | 31 | 27 | 18 | 6 | 20 |
| 22 | 18 | 30 | 51 | 49 | 35 | 50 | 25 | 8 | 10 | 26 | 31 |
| 33 | 29 | 40 | 37 | 38 | 44 | 24 | 34 | 42 | 38 | 11 | 23 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Stem-and-leaf diagram drawn | M2 A1 (any one group) | Totals in groups: 7, 8, 6, 7, 6, 9, 5, 5, 3, 3, 0, 0, 1 |
| (b) \(Q_1 = 14\), \(Q_2 = 26\), \(Q_3 = 35\) | M1 A1 A1 A1 | |
| (c) Box plot drawn | B3 B1 | Outlier at 69 |
(a) Stem-and-leaf diagram drawn | M2 A1 (any one group) | Totals in groups: 7, 8, 6, 7, 6, 9, 5, 5, 3, 3, 0, 0, 1 | A1 A1 A1 A1 A1 |
(b) $Q_1 = 14$, $Q_2 = 26$, $Q_3 = 35$ | M1 A1 A1 A1 |
(c) Box plot drawn | B3 B1 | Outlier at 69 | | Total: 16 marks
---In a survey of natural habitats, the numbers of trees in sixty equal areas of land were recorded, as follows:
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
17 & 12 & 9 & 23 & 40 & 32 & 11 & 5 & 34 & 22 & 31 & 8 \\
\hline
15 & 45 & 10 & 52 & 14 & 13 & 29 & 43 & 69 & 30 & 15 & 47 \\
\hline
35 & 6 & 24 & 13 & 19 & 26 & 9 & 31 & 27 & 18 & 6 & 20 \\
\hline
22 & 18 & 30 & 51 & 49 & 35 & 50 & 25 & 8 & 10 & 26 & 31 \\
\hline
33 & 29 & 40 & 37 & 38 & 44 & 24 & 34 & 42 & 38 & 11 & 23 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Construct a stem-and-leaf diagram to illustrate this data, using the groupings 5 - 9, 10 - 14, 15 - 19, 20 - 24, etc. [8 marks]
\item Find the three quartiles for the distribution. [4 marks]
\item On graph paper construct a box plot for the data, showing your scale and clearly indicating any outliers. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [16]}}