Question

the box plots represent the distributions of typing speeds of students before and after a computer programming course. typing speeds (words per minute) after before 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 which statement is true about the variability of the distributions? the interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course the interquartile ranges of the two distributions are the same the range of the speeds after the course is smaller than the range of the speeds before the course the ranges of the two distributions are the same

Explanation:

Step1: Recall range and IQR from box - plot

Range = Max - Min, IQR = Q3 - Q1. In a box - plot, the box represents the inter - quartile range (IQR) and the ends of the whiskers represent the range.

Step2: Analyze the box - plots visually

For the "Before" box - plot: Assume Min = 55, Q1≈65, Q3≈80, Max = 100. Range = 100 - 55=45, IQR = 80 - 65 = 15.
For the "After" box - plot: Assume Min = 60, Q1≈70, Q3≈85, Max = 105. Range = 105 - 60 = 45, IQR = 85 - 70=15.

Answer:

The interquartile ranges of the two distributions are the same.