| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Compare distributions using stem-and-leaf |
| Difficulty | Moderate -0.8 This is a routine S1 question testing standard stem-and-leaf diagram interpretation, median/quartile calculation, and box plot construction. All parts follow textbook procedures with no problem-solving required—students simply apply learned techniques systematically. The most demanding aspect is careful counting and arithmetic, making it easier than average A-level maths questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Company \(A\) | Company \(B\) | ||||||
| (3) | \(4\ 3\ 1\) | 2 | \(0\ 5\ 6\ 6\ 8\ 9\) | (6) | |||
| (4) | \(9\ 8\ 6\ 5\) | 3 | \(1\ 3\ 4\ 7\ 9\) | (5) | |||
| (4) | \(8\ 8\ 6\ 2\) | 4 | \(0\ 1\ 3\ 5\ 8\) | ( ) | |||
| (6) | \(9\ 7\ 5\ 3\ 2\ 1\) | 5 | \(2\ 6\ 8\ 9\ 9\) | ( ) | |||
| (3) | \(6\ 5\ 3\) | 6 | \(3\ 4\ 7\ 7\) | ( ) | |||
| (3) | \(3\ 2\ 2\) | 7 | \(0\ 1\ 5\) | ( ) |
| Answer | Marks |
|---|---|
| (a) \(5, 5, 4, 3\) | B1 |
| (b) For \(A\): median \(= 51\), \(Q_1 = 38\), \(Q_3 = 63\) | B1 B1 B1 |
| For \(B\): median \(= 44\), \(Q_1 = 31\), \(Q_3 = 63\) | B1 B1 B1 |
| (c) Box plots drawn, with scale shown | B3 B3 |
| (d) \(A\) has higher average and smaller interquartile range, so \(A\)'s times are higher overall but more consistent | B1 B1 |
| (e) \(A\) has slight negative skew, \(B\) has positive skew | B1 B1 |
**(a)** $5, 5, 4, 3$ | B1 |
**(b)** For $A$: median $= 51$, $Q_1 = 38$, $Q_3 = 63$ | B1 B1 B1 |
For $B$: median $= 44$, $Q_1 = 31$, $Q_3 = 63$ | B1 B1 B1 |
**(c)** Box plots drawn, with scale shown | B3 B3 |
**(d)** $A$ has higher average and smaller interquartile range, so $A$'s times are higher overall but more consistent | B1 B1 |
**(e)** $A$ has slight negative skew, $B$ has positive skew | B1 B1 |
**Total marks: 17**The back-to-back stem and leaf diagram shows the journey times, to the nearest minute, of the commuter services into a big city provided by the trains of two operating companies.
\begin{center}
\begin{tabular}{ccccccccc}
& & Company $A$ & & & Company $B$ & & \\
(3) & & $4\ 3\ 1$ & 2 & $0\ 5\ 6\ 6\ 8\ 9$ & & (6) \\
(4) & & $9\ 8\ 6\ 5$ & 3 & $1\ 3\ 4\ 7\ 9$ & & (5) \\
(4) & & $8\ 8\ 6\ 2$ & 4 & $0\ 1\ 3\ 5\ 8$ & & ( ) \\
(6) & $9\ 7\ 5\ 3\ 2\ 1$ & 5 & $2\ 6\ 8\ 9\ 9$ & & ( ) \\
(3) & & $6\ 5\ 3$ & 6 & $3\ 4\ 7\ 7$ & & ( ) \\
(3) & & $3\ 2\ 2$ & 7 & $0\ 1\ 5$ & & ( ) \\
\end{tabular}
\end{center}
Key: $4|3|6$ means 34 minutes for Company $A$ and 36 minutes for Company $B$.
\begin{enumerate}[label=(\alph*)]
\item Write down the numbers needed to complete the diagram. [1 mark]
\item Find the median and the quartiles for each company. [6 marks]
\item On graph paper, draw box plots for the two companies. Show your scale. [6 marks]
\item Use your plots to compare the two sets of data briefly. [2 marks]
\item Describe the skewness of each company's distribution of times. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q7 [17]}}