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

Explanation:

Step1: Arrange data in order

$30, 35, 35, 45, 46, 46, 52, 55, 57$

Step2: Find the minimum

The minimum value is $30$.

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

Step4: Find the median ($Q_2$)

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

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, $Q_3=\frac{52+55}{2}=53.5$.

Step6: Find the maximum

The maximum value is $57$.

A box - plot has a box from $Q_1$ to $Q_3$ with a line at the median $Q_2$, and whiskers from the box to the minimum and maximum values.

The box should start at $35$, end at $53.5$, have a line at $46$, and whiskers going to $30$ and $57$.

Answer:

We need to visually inspect the given box - plots and find the one with a minimum of $30$, $Q_1 = 35$, median of $46$, $Q_3=53.5$, and maximum of $57$. Without the ability to label the options, you would look for a box - plot with the left - hand end of the box at $35$, a vertical line in the box at $46$, the right - hand end of the box at approximately $53.5$, and whiskers extending to $30$ and $57$.