AP Statistics Curriculum 2007 EDA Shape

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* [[SOCR_EduMaterials_Activities_RNG | You can generate data using the SOCR Modeler as shown here]].
* [[SOCR_EduMaterials_Activities_RNG | You can generate data using the SOCR Modeler as shown here]].
* [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Try fitting multi-model mixture models to samples of 2 Normal distributions with very different centers]]
* [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Try fitting multi-model mixture models to samples of 2 Normal distributions with very different centers]]
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===[[EBook_Problems_EDA_Shape | Problems]]===
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Revision as of 04:39, 26 October 2009

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 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

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

Problems




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