The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?

Answer: B. 9

The median is the sixth value, 8. The median of the lower half 1, 3, 4, 6, 7 is 4, the first quartile, and the median of the upper half 10, 12, 13, 15, 20 is 13, the third quartile, so the interquartile range is 13 − 4 = 9. A box plot draws a box from the first to the third quartile with a line at the median, showing where the middle half of the data lies. There are several conventions for computing quartiles, and the functions of spreadsheet software and the like may give slightly different values.

• A. 4.5 is the quartile deviation, half of the interquartile range.
• B. Correct. 13 − 4 = 9.
• C. 20 − 1 = 19 is the difference between the maximum and minimum (the range), which for these data corresponds to the length between the ends of the whiskers.