Question

two teachers kept track of how much time each student in their homeroom class spent volunteering last month. these box plots show the results. based on the data in the box plots, determine whether each statement is true or false. statement true false one fourth of all the students in the two classes combined volunteered for at least 12 hours. there is less variation in the amount of time students in ms. avilas class spent volunteering than in the amount of time students in mr. beams class spent volunteering. students in ms. avilas class generally spent less time volunteering than students in mr. beams class did.

Explanation:

Step1: Recall box - plot properties

A box - plot divides data into quartiles. The first quartile ($Q_1$) represents the 25th percentile, the second quartile ($Q_2$ or median) represents the 50th percentile, and the third quartile ($Q_3$) represents the 75th percentile.

Step2: Analyze the first statement

For the combined data of two classes, we cannot assume that the quartiles of the combined data can be determined just by looking at the individual box - plots. Each box - plot represents the distribution within a single class. We don't know the sample sizes of each class to combine the data and find the quartiles of the combined data. So, the statement "One fourth of all the students in the two classes combined volunteered for at least 12 hours" is False.

Step3: Analyze the second statement

The inter - quartile range (IQR) is a measure of variation, $IQR = Q_3 - Q_1$. The length of the box in a box - plot represents the IQR. The box for Mr. Beam's class is shorter than the box for Ms. Avila's class. A shorter box indicates less variation in the middle 50% of the data. So, the statement "There is less variation in the amount of time students in Ms. Avila's class spent volunteering than in the amount of time students in Mr. Beam's class spent volunteering" is False.

Step4: Analyze the third statement

The median (the line inside the box) of Ms. Avila's class is higher than the median of Mr. Beam's class. This means that, generally, students in Ms. Avila's class spent more time volunteering than students in Mr. Beam's class. So, the statement "Students in Ms. Avila's class generally spent less time volunteering than students in Mr. Beam's class did" is False.

Answer:

One fourth of all the students in the two classes combined volunteered for at least 12 hours: False
There is less variation in the amount of time students in Ms. Avila's class spent volunteering than in the amount of time students in Mr. Beam's class spent volunteering: False
Students in Ms. Avila's class generally spent less time volunteering than students in Mr. Beam's class did: False