| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 14 |
| 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 question testing standard box plot construction and interpretation. Students must read a stem-and-leaf diagram, find median/quartiles (straightforward counting), draw two box plots, and make basic comparative statements. All techniques are textbook exercises with no problem-solving or novel insight required, making it easier than average. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Median \(= 15.5^{\text{th}} = \frac{31+32}{2} = 31.5\) | M1 A1 | |
| \(Q_1 = 7.75^{\text{th}} = 20\) | A1 | |
| \(Q_3 = 23.25^{\text{th}} = 45.5\) | A1 | |
| (b) [Boxplot with appropriate scale and values] | B3 | |
| (c) [Boxplot with appropriate scale and values] | B3 | |
| (d) e.g. similar range, youngest and oldest both a bit higher for E; median of M lower meaning younger students on average; IQR of M smaller meaning student ages more similar; E roughly symmetrical, M +vely skewed | B4 | (14 marks total) |
**(a)** Median $= 15.5^{\text{th}} = \frac{31+32}{2} = 31.5$ | M1 A1 |
$Q_1 = 7.75^{\text{th}} = 20$ | A1 |
$Q_3 = 23.25^{\text{th}} = 45.5$ | A1 |
**(b)** [Boxplot with appropriate scale and values] | B3 |
**(c)** [Boxplot with appropriate scale and values] | B3 |
**(d)** e.g. similar range, youngest and oldest both a bit higher for E; median of M lower meaning younger students on average; IQR of M smaller meaning student ages more similar; E roughly symmetrical, M +vely skewed | B4 | **(14 marks total)**
---A College offers evening classes in GCSE Mathematics and English.
In order to assess which age groups were reluctant to use the classes, the College collected data on the age in completed years of those currently attending each course. The results are shown in this back-to-back stem and leaf diagram.
\includegraphics{figure_4}
Key: $1 | 3 | 2$ means age 31 doing Mathematics and age 32 doing English
\begin{enumerate}[label=(\alph*)]
\item Find the median and quartiles of the age in completed years of those attending the Mathematics classes. [4 marks]
\item On graph paper, draw a box plot representing the data for the Mathematics class. [3 marks]
\end{enumerate}
The median and quartiles of the age in completed years of those attending the English classes are 25, 41 and 57 years respectively.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Draw a box plot representing the data for the English class using the same scale as for the data from the Mathematics class. [3 marks]
\item Using your box plots, compare and contrast the ages of those taking each class. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q4 [14]}}