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 definitions

Range = Max - Min, IQR = Q3 - Q1.

Step2: Analyze range for 'Before'

For before - course data, Min = 40, Max = 100, Range = 100 - 40=60.

Step3: Analyze range for 'After'

For after - course data, Min = 60, Max = 100, Range = 100 - 60 = 40. So range after < range before.

Step4: Analyze IQR for 'Before'

For before - course, Q1≈65, Q3≈85, IQR≈85 - 65 = 20.

Step5: Analyze IQR for 'After'

For after - course, Q1≈75, Q3≈85, IQR≈85 - 75 = 10. So IQR after < IQR before.

Answer:

The range of the speeds after the course is smaller than the range of the speeds before the course.