a sample of 10 bags of marbles is selected, and the number of marbles in each bag is counted. the list shows…

Explanation:

Step1: Sort the data

First, sort the data set (22,24,13,19,19,23,22,18,20,23) in ascending order: (13,18,19,19,20,22,22,23,23,24).

Step2: Find the median

Since there are (n = 10) data points (even number), the median (Q_2=\frac{20 + 22}{2}=21).

Step3: Find the lower quartile (Q_1)

The lower half of the data is (13,18,19,19,20). The median of the lower half (for (n = 5) data points, the middle value is the third one) (Q_1 = 19).

Step4: Find the upper quartile (Q_3)

The upper half of the data is (22,22,23,23,24). The median of the upper half (for (n = 5) data points, the middle value is the third one) (Q_3=23).

Step5: Find the minimum and maximum

The minimum value (min = 13) and the maximum value (max=24).

Now, in a box - plot, the box is from (Q_1) to (Q_3), the line inside the box is at (Q_2), and the whiskers go from (min) to (max).

Answer:

The box - plot with (Q_1 = 19), (Q_2=21), (Q_3 = 23), (min = 13), (max = 24) is the correct one. (Since we can't see the exact labels of the options, but based on the calculated quartiles and min - max values, the box - plot with these values is the answer)