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 $(Q_{1} and Q_{3}),$ 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.

Exercise