Question Video: Comparing the Range of Data Using a Double Box Plot | Nagwa Question Video: Comparing the Range of Data Using a Double Box Plot | Nagwa

# Question Video: Comparing the Range of Data Using a Double Box Plot Mathematics

This double box-and-whisker plot compares the prices of books in 2 bookstores. Which bookstore has a greater range of prices?

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### Video Transcript

This double box-and-whisker plot compares the prices of books in two bookstores. Which bookstore has a greater range of prices?

Let’s firstly recall the information that is shown on a box-and-whisker plot. On the 𝑥 or horizontal axis is the price of the books. This axis goes from 60 to 130 dollars. We have two bookstores. The bottom box-and-whisker plot shows the information for bookstore A and the top one for bookstore B. There are five key points on any box-and-whisker plot indicated in this case by the five dots. We have the minimum value, the lower quartile, median, upper quartile, and the maximum value. In the context of this question, the minimum is the cheapest book; the maximum is the most expensive book. The median is the price of the book, with half the books being cheaper and half the books being more expensive, if you lined all the books up in order from cheapest to most expensive.

The lower quartile is the price of the book, a quarter of the way up the list. And the upper quartile is the price of the book, three-quarters of the way up the list. 25 percent of the books are more expensive than the upper quartile, whereas 75 percent are less expensive or cheaper. It is also worth recalling that we can calculate the interquartile range or IQR by subtracting the lower quartile value from the upper quartile value. This is the range in price of the middle 50 percent of the books.

In this question, we’re asked to calculate which bookstore has a greater range of prices. The range of prices will be equal to the maximum value minus the minimum value. We subtract the cheapest price from the most expensive one. Let’s firstly consider our values from bookstore A. Bookstore A had a maximum price of 120 dollars. This is the point furthest to the right on the bottom box plot. It had a minimum or cheapest price of 75 dollars as this is the point furthest to the left. To calculate the range, we need to subtract 75 from 120. This is equal to 45. So the range of prices in bookstore A is 45 dollars.

Repeating this process for bookstore B, we have a maximum price of 105 dollars. We have a minimum or cheapest price of 65 dollars. Subtracting 65 from 105 gives us a range of prices of 40 dollars. As 45 dollars is greater than 40 dollars, we can conclude that bookstore A has the greater range of prices. This indicates that the price of books in bookstore A is more spread out than in bookstore B. Both the range and interquartile range are a measure of spread, whereas the median is a measure of average or central tendency.

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