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 data set is 30, 35, 35, 45, 46, 46, 52, 55, 57. The minimum value is 30.

Step2: 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, $Q_1=\frac{35 + 35}{2}=35$.

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 is 57. A box - plot has a box from $Q_1$ to $Q_3$ with a line at the median, and whiskers from the box to the minimum and maximum values.

Answer:

We would need to visually inspect the box - plots and check which one has a minimum value of 30, $Q_1 = 35$, median of 46, $Q_3=53.5$ and maximum of 57. Without the ability to see the actual box - plots clearly, we have provided the key values to identify the correct one. If you can describe the box - plots in terms of these values (positions of minimum, $Q_1$, median, $Q_3$, maximum), we can further assist in choosing the correct one.