# AP Statistics Curriculum 2007 EDA Shape

## Contents

## General Advance-Placement (AP) Statistics Curriculum - Measures of Shape

### Definitions

- A distribution is
**unimodal**if it has one mode. Unimodal distributions include:- Bell shaped distributions (symmetric, Normal)
- Skewed right or skewed left
- We can use the mean and median to help interpret the shape of a distribution. For an unimodal distribution we have these properties:
- If
**mean = median**, then the distribution is symmetric - If
**mean > median**, then the distribution is right skewed - If
**mean < median**, then the distribution is left skewed - Note that depending on the protocol for computing the median, these rules may be violated for certain distributions. Some examples of such violations are included in this JSE paper.

- If

**Multimodal**distributions have two or more modes. Examples of multimodal distributions are:

### Other Measures of Shape

This section also provides moment-based characterization of distribution shape.

### Examples

What seems like a logical choice for the shape of the hot dog calorie data? Try looking at the histogram of the calories for the Hot-dogs dataset.

### Activities

Collect data, draw the sample histogram or dot-plot and classify the shape of the distribution accordingly. Also, if unimodal, classify symmetry (symmetric, skewed right or skewed left).

- Data collected on height of randomly sampled college students.
- Data collected on height of randomly sampled female college students.
- The salaries of all persons employed by a large university.
- The amount of time spent by students on a difficult exam.
- The grade distribution on a difficult exam.

### Hands-on activities

- You can generate data using the SOCR Modeler as shown here.
- Try fitting multi-model mixture models to samples of 2 Normal distributions with very different centers

### Problems

- SOCR Home page: http://www.socr.ucla.edu

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