AP Statistics Curriculum 2007 EDA Shape

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 a 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

• Multimodal distributions have two or more than one modes. Examples of multimodal distributions are:
  • U Quadratic
  • Mixture Distributions

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

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

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