The box and whisker plot is a figure that displays the five-number summary of a set of data. This includes the minimum, the maximum, the upper quartile, the lower quartile, and the median.
From the data given, notice that the minimum value is 3 and the maximum value is 16.
Also, note that the numbers 9 and 10, fall in the middle. Hence, the median or the second quartile Q2 of the data is:
[tex]\begin{gathered} Q_2=\frac{9+10}{2} \\ =\frac{19}{2}=9.5 \end{gathered}[/tex]
The first quartile or the lower quartile is the median of the lower half of the data in a set.
To find the first quartile (Q1), group the data into a lower half:
[tex]3,6,6,7,8,8,9[/tex]
Notice that the median of the lower half is 7. Hence, the first quartile or the lower quartile is 7:
[tex]Q_1=7[/tex]
The upper quartile Q2 is the median of the upper half of the data.
The upper half of the data is:
[tex]10,13,13,13,14,14,16[/tex]
Notice that the median of the upper half is 13.
It follows that:
[tex]Q_3=13[/tex]
