Difference between revisions of "AP Statistics Curriculum 2007 EDA Shape"
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** Bell shaped distributions (symmetric, Normal) | ** Bell shaped distributions (symmetric, Normal) | ||
** Skewed right or skewed left | ** Skewed right or skewed left | ||
| − | ** We can use the [[AP_Statistics_Curriculum_2007_EDA_Center | mean and median]] to help interpret the shape of a distribution. For | + | ** 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: |
*** If '''mean = median''', then the distribution is symmetric | *** If '''mean = median''', then the distribution is symmetric | ||
*** If '''mean > median''', then the distribution is right skewed | *** If '''mean > median''', then the distribution is right skewed | ||
*** If '''mean < median''', then the distribution is left 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 [http://www.amstat.org/publications/jse/v13n2/vonhippel.html examples of such violations are included in this JSE paper]. | ||
| − | * '''Multimodal''' distributions have two or more | + | * '''Multimodal''' distributions have two or more modes. Examples of multimodal distributions are: |
** [http://en.wikipedia.org/wiki/U-quadratic_distribution U Quadratic] | ** [http://en.wikipedia.org/wiki/U-quadratic_distribution U Quadratic] | ||
** [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Mixture Distributions]] | ** [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Mixture Distributions]] | ||
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* SOCR Home page: http://www.socr.ucla.edu | * SOCR Home page: http://www.socr.ucla.edu | ||
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Latest revision as of 14:25, 3 March 2020
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.
- 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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