Question

A Group of students had to run 400 yards in physical education class. Their distribution times is shown on the box plot below. is the range of the distribution greater or less than the twice the interquartile range of the distribution? Justify

Answer 1

The interquartile range is given by the start and end point of just the middle box.

Looking at the box plot, the interquartile range is from 76 to 94, so the range is:

`\text{IQR}=94-76=18`

The range of the distribution is given by the start and end point of the entire plot.

So the range starts at 63 and ends at 108, so it is:

`\text{range}=108-63=45`

Comparing how many times one range is greater than the other:

`(45)/(18)=2.5`

So the range of the distribution is greater than twice the interquartile range.