In this lesson, students focus on how the mean can be described as the balance point for the distribution of a set of data.
Planning and Resources
Objectives
Students should identify the mean as the balance point of a distribution. They find and interpret deviations from the mean as a way to measure the spread of a distribution.
Vocabulary
mean
deviation
mean absolute deviation (MAD)
Standard:Search Standards Alignment
Downloads
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Lesson Snapshot
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.
