In this lesson, students explore two different representations of the mean. First, 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. This is sometimes called the “leveling out” or the “fair share” interpretation of the mean.

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 recognize that the distances on either side of the mean have the same sum. 

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.