AP Statistics Curriculum 2007 EDA Shape

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==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Measures of Shape==
==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Measures of Shape==
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===Measures of Shape===
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===Definitions===
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Example on how to attach images to Wiki documents in included below (this needs to be replaced by an appropriate figure for this section)!
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* A distribution is '''unimodal''' if it has one mode. Unimodal distributions include:
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<center>[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]</center>
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** Bell shaped distributions (symmetric, Normal)
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** Skewed right or skewed left
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** We can use the [[AP_Statistics_Curriculum_2007_EDA_Center | mean and median]] to help interpret the shape of a distribution. For an unimodal distribution we have these properties:
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*** If '''mean = median''', then the distribution is symmetric
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*** If '''mean > median''', then the distribution is right skewed
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*** If '''mean < median''', then the distribution is left skewed
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===Approach===
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* '''Multimodal''' distributions have two or more modes. Examples of multimodal distributions are:
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Models & strategies for solving the problem, data understanding & inference.  
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** [http://en.wikipedia.org/wiki/U-quadratic_distribution U Quadratic]
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** [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Mixture Distributions]]
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig9.jpg|500px]]</center>
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* TBD
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===Other Measures of Shape===
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[[AP_Statistics_Curriculum_2007_Distrib_MeanVar | This section also provides moment-based characterization of distribution shape]].
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===Model Validation===
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Checking/affirming underlying assumptions.
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* TBD
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===Computational Resources: Internet-based SOCR Tools===
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* TBD
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===Examples===
===Examples===
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Computer simulations and real observed data.  
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What seems like a logical choice for the shape of [[AP_Statistics_Curriculum_2007_EDA_Pics#Example | the hot dog calorie data]]? Try looking at the histogram of the calories for the [[SOCR_012708_ID_Data_HotDogs |Hot-dogs dataset]].
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig4.jpg|500px]]</center>
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* TBD
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===Activities===
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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).
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*Data collected on height of randomly sampled college students.
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*Data collected on height of randomly sampled female college students.
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*The salaries of all persons employed by a large university.
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*The amount of time spent by students on a difficult exam.
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*The grade distribution on a difficult exam.
   
   
===Hands-on activities===
===Hands-on activities===
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Step-by-step practice problems.  
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* [[SOCR_EduMaterials_Activities_RNG | You can generate data using the SOCR Modeler as shown here]].
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* [[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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* TBD
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<hr>
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===[[EBook_Problems_EDA_Shape | Problems]]===
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===References===
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* TBD
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<hr>
<hr>

Current revision as of 21:06, 4 June 2010

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

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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