| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Describe shape or skewness of distribution |
| Difficulty | Moderate -0.8 This is a routine S1 question testing standard data handling skills: reading stem-and-leaf diagrams, finding median/quartiles using position formulas, calculating percentiles, drawing box plots, and identifying skewness from quartile positions. All techniques are straightforward recall with no problem-solving or novel insight required, making it easier than average but not trivial due to the computational work involved. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| \(A\) | \(B\) | |
| 8, 7, 4, 1, 0 | 1 | 1, 1, 2, 5, 6, 8, 9 |
| 9, 8, 7, 6, 6, 5, 2 | 2 | 0, 3, 4, 6, 7, 7, 9 |
| 9, 7, 6, 4, 2, 1, 0 | 3 | 1, 4, 5, 5, 8 |
| 8, 6, 3, 2, 2 | 4 | 0, 2, 6, 6, 9, 9 |
| 6, 4, 0 | 5 | 2, 3, 5, 7 |
| 5, 3, 1 | 6 | 0, 1 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) A: Median = 33, \(Q_1 = 26\), \(Q_3 = 46\) | B1 B1 B1 | |
| B: Median = 34, \(Q_1 = 20\), \(Q_3 = 49\) | B1 B1 B1 | |
| (b) \(0.42 \times 30 = 12.6\), so 13th value, 30 | M1 A1 | |
| (c) Box plots drawn | B2 B2 | |
| (d) A has positive skew, B is fairly symmetric | B1 B1 | Total: 14 |
(a) A: Median = 33, $Q_1 = 26$, $Q_3 = 46$ | B1 B1 B1 |
B: Median = 34, $Q_1 = 20$, $Q_3 = 49$ | B1 B1 B1 |
(b) $0.42 \times 30 = 12.6$, so 13th value, 30 | M1 A1 |
(c) Box plots drawn | B2 B2 |
(d) A has positive skew, B is fairly symmetric | B1 B1 | **Total: 14**The stem-and-leaf diagram shows the values taken by two variables $A$ and $B$.
\begin{tabular}{c|c|c}
$A$ & & $B$ \\
\hline
8, 7, 4, 1, 0 & 1 & 1, 1, 2, 5, 6, 8, 9 \\
9, 8, 7, 6, 6, 5, 2 & 2 & 0, 3, 4, 6, 7, 7, 9 \\
9, 7, 6, 4, 2, 1, 0 & 3 & 1, 4, 5, 5, 8 \\
8, 6, 3, 2, 2 & 4 & 0, 2, 6, 6, 9, 9 \\
6, 4, 0 & 5 & 2, 3, 5, 7 \\
5, 3, 1 & 6 & 0, 1 \\
\end{tabular}
Key: 3 | 1 | 2 means $A = 13$, $B = 12$
\begin{enumerate}[label=(\alph*)]
\item For each set of data, calculate estimates of the median and the quartiles. [6 marks]
\item Calculate the 42nd percentile for $A$. [2 marks]
\item On graph paper, indicating your scale clearly, construct box and whisker plots for both sets of data. [4 marks]
\item Describe the skewness of the distribution of $A$ and of $B$. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [14]}}