Question

Just so you know you can use half numbers for example 46.5 or 24.5 etc.

Answer 1

Given:

`61,63,63,64,67,67,69,72,73,74,75,79,81,85,86,87,89,92`

To draw:

The box and whisker plot.

Step-by-step 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,

`\begin{gathered} Q_2=(((n)/(2))^(th)term+((n)/(2)+1)^(th)term)/(2) \\ =\frac{((18)/(2)){^(th)term+((18)/(2)+1)^(th)term}}{2} \\ =(9^(th)term+10^(th)term)/(2) \\ =(73+74)/(2) \\ =(147)/(2) \\ Q_2=73.5 \end{gathered}`

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,

`\begin{equation*} 61,63,63,64,67,67,69,72,73 \end{equation*}`

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,

`\begin{equation*} 74,75,79,81,85,86,87,89,92 \end{equation*}`

The middle term is 85.

Therefore, the upper quartile is 85.

So, the box and whisker plot is,