Intent

In this activity and the next, Kai and Mai Spread Data, students explore several ways to measure, in a quantitative way, the spread of a data set. These initial explorations prepare students for the introduction of standard deviation as a measure of spread.

Mathematics

Several statistics measure the spread of a data set. In this activity, students will be finding the range of the data: the numeric difference between the highest and lowest values in the set. As it uses two data points, this statistic is easily calculated. And two very differently distributed data sets can have the same range.

Progression

Students will work on Data Spread in class, and then continue with Kai and Mai Spread Data individually. Discussion in groups and as a whole class will follow.

Approximate Time

40 minutes

Classroom Organization

Groups

Doing the Activity

Introduce the activityby having the class examine and comment on the four sets of data. Bring out that the sets all have the same mean (the medians are almost the same as well) and differ mainly in how “spread out” they are.

You might also want students to consider how the data sets would look if they were displayed in frequency bar graphs. If you think it will help them, suggest they also calculate the mean, median, and mode for each set.

Discussing and Debriefing the Activity

The discussion should raise the observation that the range doesn’t take into consideration the spread of data “inside” the least and greatest values.

Key Question

Which data set seems to be the most spread out from the mean?