a data set 20, 36, 52, 56, 24, 16, 40, 4, 28 represents the number of books purchased by some book - club…

Explanation:

Step1: Sort the data

$4,16,20,24,28,36,40,52,56$

Step2: Find the minimum value

The minimum value is $4$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 9$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, $Q_1=\frac{16 + 20}{2}=18$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{9+1}{2}=5$. So, $Q_2 = 28$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(9 + 1)}{4}=7.5$. So, $Q_3=\frac{40+52}{2}=46$.

Step6: Find the maximum value

The maximum value is $56$.

Step7: Draw the box - plot

On the number line:

• Mark a point at the minimum value ($4$).
• Draw a box from $Q_1 = 18$ to $Q_3=46$.
• Draw a vertical line inside the box at the median $Q_2 = 28$.
• Mark a point at the maximum value ($56$).
• Connect the minimum and maximum values to the box with lines (whiskers).

Answer:

The box - plot is constructed as described above with minimum = 4, $Q_1=18$, median = 28, $Q_3 = 46$, and maximum = 56.