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Video: Interpreting a Box-and-Whisker Plot

Bethani Gasparine

The given box-and-whisker plot represents the test scores for a trigonometry test. Determine the percent of the scores that are greater than or equal to 65. <Figure>

03:41

Video Transcript

The given box and whisker plot represents the test scores for a trigonometry test. Determine the percent of the scores that are greater than or equal to 65.

A box and whisker plot uses a number line to show the distribution of a set of data. The box is drawn around the quartile value, and the whiskers extend from each quartile to the extreme data points that are not outliers. Let’s go ahead and label some things on our box and whisker plot.

Here we can see 60 is the minimum value and 120 is the maximum value. The lower quartile is 65 and the upper quartile is 90 and 70 is our median. So these are simply the names of all of these blue points that are listed. So what are they? Let’s begin with the median.

The median is located right in the middle. Now it may not be in the middle of the box. However, it separates the set of data into two equal parts. So from the median value to the maximum value, that’s exactly half of the amount of test scores. So it’s 50 percent of all of the scores. And from the median to the minimum value, that would be the other half, the other 50 percent of the test scores, making the entire box and whisker plot the 100 percent. Now let’s look at the upper and the lower quartile.

The median of the lower half of the set of data is called the lower quartile. So it’s in the middle of the lower half of the data. And the middle of that 50 percent would be at the 25 percent mark. Essentially, the lower quartile is gonna be located in the middle of the lower half of the data. So on each side of that quartile will be 25 percent of the entire set of data. The upper quartile is the exact same thing but on the top half, the upper half of the set of data. So on each side of that quartile will be 25 percent. And in the middle of these two quartiles, again, it’s the median. So here we have all 100 percent of the data.

Let’s go ahead and label these percentages on the box and whisker plot. So what did these percentages mean? Well, the 25 percent means 25 percent of all of the students scored in each of these ranges. So for example, 25 percent of the students score between 70 and 90. So our question is asking to determine the percent of the scores that are greater than or equal to 65. So here we can see 65 and greater than 65 would be 25 percent plus another 25 percent plus another 25 percent, which would be equal to 75 percent.

This means 75 percent of the students scored 65 or greater, so it’s 65 or better on their trigonometry test.