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 first half of the data is (30,35,35,45). The median of this half is (\frac{35 + 35}{2}=35).

Step3: Find the median ((Q_2))

The data set has (n = 9) values. The median is the (\left(\frac{n + 1}{2}\right)) - th value. So, the median is the (5) - th value, which is (46).

Step4: Find the third quartile ((Q_3))

The second half of the data is (52,55,57). The median of this half is (55).

Step5: Find the maximum value

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

Now, check each box - plot for the correct values of minimum ((30)), (Q_1(35)), median ((46)), (Q_3(55)) and maximum ((57)).

Answer:

The box - plot with minimum at (30), (Q_1) at (35), median at (46), (Q_3) at (55) and maximum at (57) is the correct one. (Since the options are not labeled with letters, but by following the calculation of (min = 30), (Q_1=35), (Q_2 = 46), (Q_3=55), (max = 57) one can identify the correct box - plot among the given visual options)