| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring students to construct a box plot from given five-number summary statistics and make basic comments about skewness. The outlier calculation is routine (IQR = 16, so 1.5×IQR = 24, making 63 an outlier), and the interpretation requires only standard textbook observations about positive skew. No problem-solving or novel insight needed—pure procedural application. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers |
| Answer | Marks |
|---|---|
| \((X = 3) \cap (X = 1)\) | \(0.1 \times 0.3 = 0.03\) |
| \((X = 1) \cap (X = 3)\) | \(0.3 \times 0.1 = 0.03\) |
| \((X = 2) \cap (X = 2)\) | \(0.2 \times 0.2 = 0.04\) |
Question 4:
$(X = 3) \cap (X = 1)$ | $0.1 \times 0.3 = 0.03$
$(X = 1) \cap (X = 3)$ | $0.3 \times 0.1 = 0.03$
$(X = 2) \cap (X = 2)$ | $0.2 \times 0.2 = 0.04$4. Aeroplanes fly from City $A$ to City $B$. Over a long period of time the number of minutes delay in take-off from City $A$ was recorded. The minimum delay was 5 minutes and the maximum delay was 63 minutes. A quarter of all delays were at most 12 minutes, half were at most 17 minutes and $75 \%$ were at most 28 minutes. Only one of the delays was longer than 45 minutes.
An outlier is an observation that falls either $1.5 \times$ (interquartile range) above the upper quartile or $1.5 \times$ (interquartile range) below the lower quartile.
\begin{enumerate}[label=(\alph*)]
\item On the graph paper opposite draw a box plot to represent these data.
\item Comment on the distribution of delays. Justify your answer.
\item Suggest how the distribution might be interpreted by a passenger who frequently flies from City $A$ to City $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{3d4f7bfb-b235-418a-9411-a4d0b3188254-008_1190_1487_278_223}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q4}}