2. Two youth clubs, Eastyou and Westyou, decided to raise money for charity by running a 5 km race. All the members of the youth clubs took part and the time, in minutes, taken for each member to run the 5 km was recorded.
The times for the Westyou members are summarised in Figure 1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b115bffa-1190-4a2b-b6f2-b006580e8dbd-06_349_1378_497_274}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
- Write down the time that is exceeded by \(75 \%\) of Westyou members.
The times for the Eastyou members are summarised by the stem and leaf diagram below.
| Stem | Leaf | | | | | | | | | | | | | |
| 2 | 0 | 2 | 3 | 4 | | | | | | | | | | | \(( 4 )\) | | | | | | | | | | | | | | | |
| 2 | 5 | 6 | 8 | 8 | 8 | 9 | 9 | | | | | | | | | | | | | | | | | | | | | | | |
| 3 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 4 | \(( 14 )\) | | | | | | | | | | | | | | | |
| 3 | 5 | 5 | 5 | 7 | 9 | | | | | | | | | | \(( 5 )\) | | | | | | | | | | | | | | | |
Key: 2|0 means 20 minutes - Find the value of the median and interquartile range for the Eastyou members.
An outlier is a value that falls either
- On the grid on page 7, draw a box plot to represent the times of the Eastyou members.
- State the skewness of each distribution. Give reasons for your answers.
$$\begin{aligned}
& \text { more than } 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right) \text { above } Q _ { 3 }
& \text { or more than } 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right) \text { below } Q _ { 1 }
\end{aligned}$$
\includegraphics[max width=\textwidth, alt={}]{b115bffa-1190-4a2b-b6f2-b006580e8dbd-06_2255_50_314_1976}
\includegraphics[max width=\textwidth, alt={}, center]{b115bffa-1190-4a2b-b6f2-b006580e8dbd-07_406_1390_2224_262}
Turn over for a spare grid if you need to redraw your box plot.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Only use this grid if you need to redraw your box plot.}
\includegraphics[alt={},max width=\textwidth]{b115bffa-1190-4a2b-b6f2-b006580e8dbd-09_401_1399_2261_258}
\end{figure}