# Class 09: Topic 8: Measures of Center

This outline is also available in PDF.

Held: Monday, 11 February 2008

Summary: We consider more ways to talk about distributions, particularly ways to identify the center of a distribution.

Notes:

• Homework for Wednesday: Activities 8-9, 8-17, 8-18, 8-22, 8-23. The quiz percentages file for 8-17 is stored in `/home/rebelsky/Stats115/Data/MarriageAges.csv`. The quiz percentages file for 8-18 is stored in `/home/rebelsky/Stats115/Data/QuizPct.csv`.
• Preparation for Wednesday: Overview and Preliminaries 1-3 for Topic 9.
• I plan to assign partners for this week of class.
• Homeworks for sections 3, 4, and 5 returned. We'll discuss some issues.
• Dumb question: Why, when I added the length of monarch reigns to 1066, did I not get the year in which Elizabeth II's reign began?
• Preparation: Overview and Preliminaries for Topic 8.
• Handouts: R notes on activiy 8.
• Due: Activities 6-26, 6-30, 7-8, 7-12.

Overview:

• A few past topics: Homework, skew, etc.
• Ways to think about center.

## Notes on Homework

• I noted some potential academic honesty issues on Topic 3
• It's fine if you work together
• But you must mention on your work that you worked together.

## Notes on Previous Topics

• Did anyone have any questions about the figure on p. 103.
• How should you arrange a two-way table? Which are the rows, which are the columns?

## A Note on Skewness

• A few of you have noted that skewness seems backwards, because a chart in which most of the data are clumped to the left is skewed right, and vice versa.
• But skewness is really supposed to describe what a distribution l behaves relative to a symmetric distribution (more precisely, a normal distribution).
• A distribution that is skewed right has extra data points to the right.
• A distribution that is skewed left has extra data points to the left.
• You can also think of skewness in terms of its effect on the mean: In a distribution that is skewed right, the mean is to the right of the median.

## Measures of Center

• As you may recall, we have been talking informally about the center of a distribution
• Today, we look more formally at those issues.

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

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Samuel A. Rebelsky, rebelsky@grinnell.edu

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