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 inter - quartile range (IQR) concept

IQR = Q3 - Q1 for a box - plot.

Step2: Observe box - plots

For both before and after box - plots, the length of the box (which represents IQR) is the same.

Step3: Recall range concept

Range = Max - Min. The lengths from end - to - end of the whiskers (for range) are different for before and after. So, range statements are incorrect. Since the box lengths are equal, the IQRs are the same.

Answer:

The interquartile ranges of the two distributions are the same