Statistics and Probability / Mean as Balance Point

Understanding

The mean is the balance point of a distribution; the sum of the absolute deviations for values below the mean is equal to the sum of the absolute deviations for values above the mean.

What to look for

Have the students think about the number of steps that the teams in last place are from 6. Depending on your focus, you can introduce the concept of absolute value or you can just refer to distance as always being positive.

Sample Assessment

Given the set {1, 5, 7, 7, 10}, if you add the value 6 to the data, the mean absolute deviation will?
a. Increase
b. Decrease
c. Remain unchanged
d. There is not enough information to tell how the value will affect the mean absolute deviation.

Answer: B

The Big Idea

The mean is the balance point of a data distribution of data as well as a center of the distribution.

What are the students doing?

Students investigate the spread around the mean, which is typically measured in terms of how far the data values deviate from the mean.

What is the teacher doing?

Push students to figure out how they would order the teams in some consistent way to rank the teams.