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. 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. the student who volunteered the least number of hours is in ms. avilas class. students in ms. avilas class generally spent less time volunteering than students in mr. beams class did.

Explanation:

Statement 1: One - fourth of all the students in the two classes combined volunteered for at least 12 hours.

• Box - plots represent the distribution of data for a single set of data (a single class in this case). We cannot combine the two box - plots in the way described (by taking one - fourth of the combined data) just from looking at two separate box - plots. We don't know the number of students in each class. So, this statement is false.

Statement 2: 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.

• The inter - quartile range (IQR, the length of the box in a box - plot) is a measure of variation. For Ms. Avila's class, if we assume the box - plot has a smaller IQR (the length of the red box is smaller than the blue box), the variation (measured by IQR) is less. So, this statement is true.

Statement 3: The student who volunteered the least number of hours is in Ms. Avila's class.

• Looking at the left - most whisker (the minimum value in the box - plot), Mr. Beam's class has a minimum value that is less than Ms. Avila's class (the left - most point of Mr. Beam's plot is to the left of Ms. Avila's left - most point). So, this statement is false.

Statement 4: Students in Ms. Avila's class generally spent less time volunteering than students in Mr. Beam's class did.

• The median (the line inside the box of the box - plot) of Ms. Avila's class is less than the median of Mr. Beam's class. The median represents the "typical" value. So, students in Ms. Avila's class generally spent less time volunteering. This statement is true.

Answer:

1. False
2. True
3. False
4. True