## 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