3 Two machines, \(A\) and \(B\), produce metal rods of a certain type. The lengths, in metres, of 19 rods produced by machine \(A\) and 19 rods produced by machine \(B\) are shown in the following back-to-back stem-and-leaf diagram.
\begin{table}[h]
| \(A\) | \(B\) |
| | | | | | 21 | 1 | 2 | 4 | | | |
| | 7 | 6 | 3 | 0 | 22 | 2 | 4 | 5 | 5 | 6 | |
| | | | | | | | | | | | |
| 8 | 7 | 4 | 3 | 1 | 1 | 23 | 0 | 2 | 6 | 8 | 9 | |
| 5 | 5 | 5 | 3 | 2 | 24 | 3 | 3 | 4 | 6 | | |
| | 4 | 3 | 1 | 0 | 25 | 6 | | | | | |
\captionsetup{labelformat=empty}
\caption{Key: 7 | 22 | 4 means 0.227 m for machine \(A\) and 0.224 m for machine \(B\).}
\end{table}
- Find the median and the interquartile range for machine \(A\).
It is given that for machine \(B\) the median is 0.232 m , the lower quartile is 0.224 m and the upper quartile is 0.243 m . - Draw box-and-whisker plots for \(A\) and \(B\).
\includegraphics[max width=\textwidth, alt={}, center]{a3b3ebd1-db9e-4552-9abe-bfdeba786d02-05_812_1205_616_511} - Hence make two comparisons between the lengths of the rods produced by machine \(A\) and those produced by machine \(B\).