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Private: Learning Math: Data Analysis, Statistics, and Probability
Variation About the Mean
Explore the concept of the mean and how variation in data can be described relative to the mean. Concepts include fair and unfair allocations, and how to measure variation about the mean.
In This Session
Part A: Fair Allocations
Part B: Unfair Allocation
Part C: Using Line Plots
Part D: Deviations from the Mean
Part E: Measuring Variation
Homework
In Session 4, we explored the Five-Number Summary and its graphical representation, the box plot. We also explored the median, a common numerical summary for a data set.
In this session, we’ll investigate another common numerical summary, the mean. We’ll also learn several ways to describe the degree of variation in data, based on how much the data values vary from the mean. See Note 1.
You will need to have these materials in hand before you begin:
- 45 coins
- calculator
- several pieces of blank paper or 22″ by 28″ poster board
- self-adhesive colored dots or 2″ by 1.5″ adhesive notepaper squares
In this session, you will do the following:
- Understand the mean as an indicator of fair allocation
- Explore deviations of data values from the mean
- Understand the mean as the “balancing point” of a data set
- Learn how to measure variation about the mean
Key Terms
Previously Introduced:
New in This Session:
allocation
deviation from the mean
equal-shares allocation
mean
mean absolute deviation (MAD)
standard deviation
variance
