Exercise 2 Page 339

To find how can we use a box-and-whisker plot to describe a data set, let's describe each of its elements. A box-and-whisker plot shows the variability of a data set along a number line. It uses a rectangular box and two segments. These segments are called whiskers.

• The box extends from the first to the third quartiles $(Q_1\text{ and }{Q}_3),$ with a line in the middle indicating the median $(Q_2)$ of the data.
• The first quartile is the median of the lower half of the data and the third quartile is the median of the upper half of the data.
• The first segment extends from the least value of the data to $Q_1,$ while the second one extends from $Q_3$ to the greatest value of the data.

The set of numbers used to draw the box plot is called the five-number summary of the data set. Each of the five numbers is labeled accordingly.

Therefore, we can use a box-and-whisker plot to show the least value, first quartile, median, second quartile, and greatest value of a data set. Additionally, by only looking at the box-and-whisker plot, we can state some facts about the data set.

• If the box and whisker to the left of the median are approximately of the same size than those to the right, the data is symmetric.
• If the length of the box and whisker on the left of the median are a noticeably different size than those on the right, the data set is skewed.
• If the whiskers are very long, the data might have outliers.
• The difference between the greatest value and the least value indicates the range of the data set.
• The difference between the third quartile and the first quartile indicates the interquartile range of the data set.