Lesson 4

In this lesson, students find and interpret the mean of a distribution (MP2) as the amount each member of the group would get if everything is distributed equally and as a balance point of a numerical distribution. The first technique is sometimes called the “leveling out” or the “fair share” interpretation of the mean. For a quantity that cannot actually be redistributed, like the weights of the dogs in a group, this interpretation translates into a thought experiment.

Suppose all of the dogs in a group had different weights and their combined weight was 200 pounds. The mean would be the weight of the dogs if all the dogs were replaced with the same number of identical dogs and the total weight was still 200 pounds.

Then, students use the structure of the data (MP7) to interpret the mean as the balance point of a numerical distribution. They calculate how far away each data point is from the mean and study how the distances on either side of the mean compare.

Students connect this interpretation to why we call the mean a measure of the center of a distribution and, through this interpretation, begin to see how the mean is useful in characterizing a “typical” value for the group. Students continue to practice calculating the mean of a data set (MP8) and interpreting it in context (MP2).