In this lesson, students learn that they can further decompose a data set into four equal groups and use the quartiles to describe a distribution. They learn that the three quartiles along with the maximum and minimum values of the data set make up a five-number summary.

Students also explore the range and interquartile range (IQR) of a distribution as two ways to measure its spread. Students reason abstractly and quantitatively (MP2) as they find and interpret the IQR as describing the distribution of the middle half of the data.

Then students use the five-number summary to construct a box plot. They make sense of the structure of a box plot on paper (MP7). They notice that, unlike the dot plot, it is not possible to know all the data points from a box plot. They understand that the box plot summarizes a data set by showing the range of the data, where the middle half of the data set is located, and how the values are divided into quarters by the quartiles.

An optional activity introduces the structure of a box plot kinesthetically, by having students position themselves on a number line on the ground.