Given:
[tex]61,63,63,64,67,67,69,72,73,74,75,79,81,85,86,87,89,92[/tex]
To draw:
The box and whisker plot.
Explanation:
According to the given data,
The minimum of the data is 61.
The maximum of the data is 92.
Since the total number of data is n = 18 which is even.
So, the median formula is given by,
[tex]\begin{gathered} Q_2=\frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2} \\ =\frac{(\frac{18}{2}){^{th}term+(\frac{18}{2}+1)^{th}term}}{2} \\ =\frac{9^{th}term+10^{th}term}{2} \\ =\frac{73+74}{2} \\ =\frac{147}{2} \\ Q_2=73.5 \end{gathered}[/tex]
Therefore, the median is 73.5.
Then, the lower quartile is the median of the lower half of the data.
The lower half data are,
[tex]\begin{equation*} 61,63,63,64,67,67,69,72,73 \end{equation*}[/tex]
The middle term is 67.
Therefore, the lower quartile is 67.
The upper quartile is the median of the upper half of the data.
The upper half data are,
[tex]\begin{equation*} 74,75,79,81,85,86,87,89,92 \end{equation*}[/tex]
The middle term is 85.
Therefore, the upper quartile is 85.
So, the box and whisker plot is,
