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) and range definitions

IQR is $Q3 - Q1$ (difference between third and first quartiles), range is $max - min$.

Step2: Analyze box - plots for IQR

For box - plots, length of box represents IQR. Visually, lengths of boxes for before and after are the same. So, $IQR_{after}=IQR_{before}$.

Step3: Analyze box - plots for range

For before: $min\approx45$, $max\approx100$, range $\approx100 - 45=55$. For after: $min\approx60$, $max\approx105$, range $\approx105 - 60 = 45$. So, range$_{after}

Answer:

The interquartile ranges of the two distributions are the same.