mr. larson, a math teacher, assigned his students a project to do in pairs. he recorded the grade each pair…

Explanation:

Step1: Arrange data in ascending order

70, 71, 73, 75, 77, 80, 84, 86, 87, 92, 95, 96, 97, 100

Step2: Find the minimum value

The minimum value is 70.

Step3: Find the first - quartile ($Q_1$)

There are 14 data points. The position of $Q_1$ is $\frac{14 + 1}{4}=3.75$. So, $Q_1$ is between the 3rd and 4th ordered data points. $Q_1=\frac{73 + 75}{2}=74$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{14}{2}=7$th and 8th ordered data points. $Q_2=\frac{84+86}{2}=85$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $3\times\frac{14 + 1}{4}=11.25$. So, $Q_3$ is between the 11th and 12th ordered data points. $Q_3=\frac{95+96}{2}=95.5$.

Step6: Find the maximum value

The maximum value is 100.

The box - plot should have the minimum value at 70, $Q_1$ at 74, median at 85, $Q_3$ at 95.5 and maximum at 100. By comparing the box - plots (not shown in full detail here but based on these values), we can determine the correct one.

Answer:

We need to compare the calculated values of minimum, $Q_1$, median, $Q_3$ and maximum with the box - plots given. Without the full visual comparison of the box - plots, we can't give a definite answer from the text description alone. But the correct box - plot should have whiskers at 70 and 100, the left - hand side of the box at approximately 74, the line inside the box at 85 and the right - hand side of the box at approximately 95.5.