2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{70137e9a-0a6b-48b5-8dd4-c436cb063351-04_284_1244_260_388}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows part of a box and whisker plot for the marks in an examination with a large number of candidates. Part of the lower whisker has been torn off.
- Given that \(75 \%\) of the candidates passed the examination, state the lowest mark for the award of a pass.
- Given that the top \(25 \%\) of the candidates achieved a merit grade, state the lowest mark for the award of a merit grade.
An outlier is defined as any value greater than \(c\) or any value less than \(d\) where
$$\begin{aligned}
& c = Q _ { 3 } + 1.5 \left( Q _ { 3 } - Q _ { 1 } \right)
& d = Q _ { 1 } - 1.5 \left( Q _ { 3 } - Q _ { 1 } \right)
\end{aligned}$$ - Find the value of \(c\) and the value of \(d\).
- Write down the 3 highest marks scored in the examination.
The 3 lowest marks in the examination were 5, 10 and 15
- On the diagram on page 7, complete the box and whisker plot.
Three candidates are selected at random from those who took this examination.
- Find the probability that all 3 of these candidates passed the examination but only 2 achieved a merit grade.
\includegraphics[max width=\textwidth, alt={}, center]{70137e9a-0a6b-48b5-8dd4-c436cb063351-05_285_1628_2343_166}
Turn over for a spare diagram if you need to redraw your plot.