the box plots represent the distributions of typing speeds of students before and after a computer…

the box plots represent the distributions of typing speeds of students before and after a computer - programming course.\ntyping speeds (words per minute)\nafter\nbefore\n40 45 50 55 60 65 70 75 80 85 90 95 100 105 110\nwhich statement is true about the variability of the distributions?\nthe interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course.\nthe interquartile ranges of the two distributions are the same.\nthe range of the speeds after the course is smaller than the range of the speeds before the course.\nthe ranges of the two distributions are the same.

the box plots represent the distributions of typing speeds of students before and after a computer - programming course.\ntyping speeds (words per minute)\nafter\nbefore\n40 45 50 55 60 65 70 75 80 85 90 95 100 105 110\nwhich statement is true about the variability of the distributions?\nthe interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course.\nthe interquartile ranges of the two distributions are the same.\nthe range of the speeds after the course is smaller than the range of the speeds before the course.\nthe ranges of the two distributions are the same.

Answer

Explanation:

Step1: Recall inter - quartile range (IQR) and range formulas

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

Step2: Analyze box - plot for before course

For the "Before" box - plot, assume Q1 = 60, Q3 = 80, Min = 55, Max = 90. Then IQR_before=80 - 60=20, Range_before=90 - 55 = 35.

Step3: Analyze box - plot for after course

For the "After" box - plot, assume Q1 = 70, Q3 = 85, Min = 65, Max = 95. Then IQR_after=85 - 70=15, Range_after=95 - 65 = 30.

Step4: Compare values

IQR_before = 20, IQR_after = 15, so IQR_after < IQR_before. Range_before = 35, Range_after = 30, so Range_after < Range_before.

Answer:

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