the data set represents the number of minutes dan spent on his homework each night. 30, 35, 35, 45, 46, 46…

Explanation:

Step1: Find the minimum value

The minimum value of the data - set (30,35,35,45,46,46,52,55,57) is (30).

Step2: Find the first quartile ((Q_1))

The data - set has (n = 9) values. The position of (Q_1) is (\frac{n + 1}{4}=\frac{9+1}{4}=2.5). So, (Q_1=\frac{35 + 35}{2}=35).

Step3: Find the median ((Q_2))

The position of the median is (\frac{n + 1}{2}=\frac{9+1}{2}=5). So, (Q_2 = 46).

Step4: 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{52+55}{2}=53.5).

Step5: Find the maximum value

The maximum value of the data - set is (57).

A box - plot has a left - most point at the minimum value ((30)), the left - hand side of the box at (Q_1 = 35), the line inside the box at (Q_2=46), the right - hand side of the box at (Q_3 = 53.5), and the right - most point at the maximum value ((57)).

Answer:

We need to visually inspect the box - plots to find the one that has the minimum at (30), (Q_1) at (35), median at (46), (Q_3) at (53.5), and maximum at (57). Without the ability to label the box - plots with letters, we can't give a lettered answer, but you should look for a box - plot with these characteristics.