The test scores for a physics test are displayed in the following box-and-whisker plot. Determine the percent of students who had scores between 85 and 120.
A box-and-whisker plot is a visual representation of the quartiles of our data. Quartiles are the values that divide a list of numbers into quarters, into fourths. On our box-and-whisker plot, the point at 85 represents the first quartile. And so we can say that one-fourth of the data fell between 70 and 85. Our second quartile, quartile two, is at 95. And that means that one-fourth of the scores fell between 85 and 95. Another fourth fell between 95 and 100. And the final fourth fell between 100 and 120.
We′re interested in the percent of students who scored between 85 and 120. This is the students between quartile one and quartile four. One-fourth plus one-fourth plus one-fourth equals three-fourths. We can say that three-fourths of students scored between 85 and 120. But our question is asking for the percent of students. And that means we need to write three-fourths as a percent.
One way to find this is to remember that percent is out of 100. So we can convert three-fourths to a fraction out of 100. Four times 25 equals 100. And if we multiply the denominator by 25, we need to multiply the numerator by 25. Three times 25 is 75. And 75 out of 100 written as a percent is 75 percent. We can say that 75 percent of the students scored between 85 and 120.