| 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 handling question requiring standard procedures: constructing a stem-and-leaf diagram, finding quartiles from ordered data, drawing a box plot, and identifying skewness. All techniques are straightforward applications of taught methods with no problem-solving or insight required, making it easier than average but not trivial due to the data organization required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 12 | 20 | 19 | 31 | 32 | 35 | 37 | 29 | 26 | 27 | 20 | 17 |
| 15 | 9 | 8 | 11 | 13 | 17 | 17 | 21 | 25 | 27 | 28 | 25 |
| 30 | 32 | 37 | 40 | 45 | 45 | 44 | 47 | 42 | 41 | 36 | 38 |
| 35 | 34 | 30 | 30 | 27 | 26 | 29 | 24 | 23 | 21 | 21 | 18 |
| 16 | 16 | 19 | 22 | 26 | 28 | 23 | 17 | 15 | 10 | 12 | 13 |
| Answer | Marks |
|---|---|
| (a) Diagram: totals in groups 2, 6, 11, 9, 12, 7, 6, 4, 3; key | \(M2\) \(A4\) \(B1\) |
| (b) \(Q_1 \approx 17\) | \(M1\) \(A1\) \(A1\) \(A1\) |
| \(Q_2 = 25.5\) | |
| \(Q_3 = 32\) | |
| (c) Box plot drawn | \(B4\) |
| (d) Negative skew | \(B1\) |
**(a)** Diagram: totals in groups 2, 6, 11, 9, 12, 7, 6, 4, 3; key | $M2$ $A4$ $B1$ |
**(b)** $Q_1 \approx 17$ | $M1$ $A1$ $A1$ $A1$ |
$Q_2 = 25.5$ | |
$Q_3 = 32$ | |
**(c)** Box plot drawn | $B4$ |
**(d)** Negative skew | $B1$ |
**Total: 16 marks**The following data were collected by counting the number of cars that passed the gates of a college in 60 successive 5 minute intervals.
\begin{tabular}{cccccccccccc}
12 & 20 & 19 & 31 & 32 & 35 & 37 & 29 & 26 & 27 & 20 & 17 \\
15 & 9 & 8 & 11 & 13 & 17 & 17 & 21 & 25 & 27 & 28 & 25 \\
30 & 32 & 37 & 40 & 45 & 45 & 44 & 47 & 42 & 41 & 36 & 38 \\
35 & 34 & 30 & 30 & 27 & 26 & 29 & 24 & 23 & 21 & 21 & 18 \\
16 & 16 & 19 & 22 & 26 & 28 & 23 & 17 & 15 & 10 & 12 & 13 \\
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Make a stem and leaf diagram for this data, using the groups $5-9$, $10-14$, $\ldots$, $45-49$. Show the total in each group and give a key to the diagram. [7 marks]
\item Find the three quartiles for this data. [4 marks]
\item On graph paper, draw a box plot for the data. [4 marks]
\item Describe the skewness of the distribution. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [16]}}