### 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.