In the previous lessons in this statistics intermediate course, we've focused entirely on summarizing distributions using the mean, the weighted mean, the median, in the mode. An interesting distribution property that hasn't been discussed yet is variability.

In this lesson, we will learn how to measure variability using range, mean absolute deviation variance, and standard deviation. You will find out why it's a good idea to summarize a distribution using variability as opposed to using just the summary metrics we've learned so far: the mean, the median, and the mode.

Not only will you learn how to calculate variance and standard deviation, you will also learn how the formulas for each are derived to get an idea of what's happening behind the scenes. You will learn about Besel's correction, which explains a small variation in the standard deviation formula.

While exploring how different measures of variability to represent a distribution, we'll work with a dataset that describes characteristics of houses sold between 2006 and 2010 in Ames, Iowa.

As you work through each concept, you’ll apply what you’ve learned from within your browser; there's no need to use your own machine to do the exercises. The Python environment inside of this course includes answer-checking to ensure you've fully mastered each concept before moving on to the next.

#### Objectives

#### Lesson Outline

1. The Range

2. The Average Distance

3. Mean Absolute Deviation

4. Variance

5. Standard Deviation

6. Average Variability Around the Mean

7. A Measure of Spread

8. The Sample Standard Deviation

9. Bessel's Correction

10. Standard Notation

11. Sample Variance — Unbiased Estimator

12. Next steps

13. Takeaways