| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 10 |
| 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 extract five-number summary from text, calculate IQR to identify outliers using a given formula, draw a standard box plot, and make basic comments about skewness. All steps are routine recall and application of standard procedures with no problem-solving or novel insight required. |
| Spec | 2.02h Recognize outliers2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| \(1.5(Q_3 - Q_1) = 1.5(28 - 12) = 24\) | B1 | May be implied |
| \(Q_3 + 24 = 52 \Rightarrow 63\) is an outlier | M1, A1 | att \(Q3 +...\) or \(Q1 -...\); 52 and \(-12\) or \(<0\) or evidence of no lower outliers |
| \(Q_1 - 24 < 0 \Rightarrow\) no outliers | A1 | 63 is an outlier |
| M1, A1, A1 |
| Answer | Marks |
|---|---|
| Distribution is +ve skew; \(Q_2 - Q_1\ (5) < Q_3 - Q_2\ (11)\) | B1; B1 |
| Answer | Marks |
|---|---|
| Many delays are small so passengers should find these acceptable, or sensible comment in context | B1 |
# Question 4:
## Part (a)
$1.5(Q_3 - Q_1) = 1.5(28 - 12) = 24$ | B1 | May be implied
$Q_3 + 24 = 52 \Rightarrow 63$ is an outlier | M1, A1 | att $Q3 +...$ or $Q1 -...$; 52 and $-12$ or $<0$ or evidence of no lower outliers
$Q_1 - 24 < 0 \Rightarrow$ no outliers | A1 | 63 is an outlier
| M1, A1, A1 |
## Part (b)
Distribution is +ve skew; $Q_2 - Q_1\ (5) < Q_3 - Q_2\ (11)$ | B1; B1 |
## Part (c)
Many delays are small so passengers should find these acceptable, or sensible comment in context | B1 |
---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]{9698650f-ef85-468d-a703-1b40df7f9d02-07_1190_1487_278_223}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2005 Q4 [10]}}