The box plot represent the distribution of typing speeds of students before and after a computer-programming course. which statement is true about the vulnerability of the distributions?

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

step-by-step explanation:

we have been given two box plots and we are asked to find the true statement about the variability of the distributions.

1. the inter quartile range of the typing speed after the course is greater than the interquartile range of the speeds before the course.

let us find interquartile range of both box plots using interquartile range formula: .  

we can see that iqr of typing speed before the course is 25 and after the course is 15, therefore, 1st statement is false.

2. the interquartile ranges of both distributions are the same.

we have seen that iqr of typing speed before the course is 25 and after the course is 15, therefore, 2nd statement is false.

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

let us find range of our both distributions.

we can see that range of the speeds after the course is 45 and the range of the speeds before the course is 50, therefore 3rd statement is true about the variability of the distributions.

4. the ranges of two distributions are the same.

we have seen that range of typing speed before the course is 50 and after the course is 45, therefore, 4th statement is false.  

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