282 Part 4: The State of the World
Suppose you had collected the data below and wanted to find the quartiles.
Number of books read last year: 16, 23, 13, 24, 25, 16, 17, 28, 19, 14, 12, 22, 13, 24, 15, 26, 27, 18, 29
Start by finding the median. Put the data in order, and find the middle value.
12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 22, 23, 24, 24, 25, 26, 27, 28, 29
There are 19 numbers, so the tenth number is the median. That’s 19. Then look at the numbers
below the median, and find the middle value in that group. That value, 15, is the first quartile.
Finally, look at the numbers above the median and find the middle value in that group. The
number 25 is the third quartile.Boxplots
One of the ways in which quartiles are used is in the creation of a graph called a box and whisker
plot, or a boxplot. It gets its name from its appearance. It’s a box with a line poking out on each
side, like a whisker. The whiskers reach to the lowest and the highest numbers in the data set, but
the box shows the quartiles.
You have the data above on number of books read, and you know that Q1 = 15, the median is 19
and Q3 = 25. Notice that the smallest value is 12 and the largest is 29. Draw a scale and mark it to
show at least 12 to 29. Draw a rectangle that reaches from 15 to 25. That’s the box part of the box
plot. From the lower end of the box, draw a line, a whisker, down to the minimum of 12. From the
upper end, draw a whisker to the maximum of 29. Finally, add a divider to the rectangle at 19 to
show where the median is.0 214 6 82011214 16 820 22 426 28 30 32