# AP Statistics Curriculum 2007 EDA Shape

(Difference between revisions)
 Revision as of 00:24, 28 January 2008 (view source)IvoDinov (Talk | contribs)← Older edit Current revision as of 21:08, 4 June 2010 (view source)Jenny (Talk | contribs) (→Definitions) (7 intermediate revisions not shown) Line 4: Line 4: * A distribution is '''unimodal''' if it has one mode. Unimodal distributions include: * A distribution is '''unimodal''' if it has one mode. Unimodal distributions include: ** Bell shaped distributions (symmetric, Normal) ** Bell shaped distributions (symmetric, Normal) - ** Skewed right + ** Skewed right or skewed left - **Skewed Left + ** 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: - * '''Multimodal''' distributions have two or more than one modes. Examples of multimodal distributions are: + *** If '''mean = median''', then the distribution is symmetric - ** [[http://en.wikipedia.org/wiki/U-quadratic_distribution | U Quadratic]] + *** If '''mean > median''', then the distribution is right skewed + *** If '''mean < median''', then the distribution is left skewed + + * '''Multimodal''' distributions have two or more modes. Examples of multimodal distributions are: + ** [http://en.wikipedia.org/wiki/U-quadratic_distribution U Quadratic] ** [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Mixture Distributions]] ** [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | Mixture Distributions]] +
[[Image:SOCR_EBook_Dinov_EDA_012708_Fig9.jpg|500px]]
+ + ===Other Measures of Shape=== + [[AP_Statistics_Curriculum_2007_Distrib_MeanVar | This section also provides moment-based characterization of distribution shape]]. ===Examples=== ===Examples=== Line 15: Line 23: ===Activities=== ===Activities=== - Classify and draw a sketch each of the following scenarios with respect to mode.  Also, if unimodal, classify symmetry (symmetric, skewed right or skewed left). + 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 college students. - Data collected on height of randomly sampled female college students. + *Data collected on height of randomly sampled female college students. - The salaries of all persons employed by a large university. + *The salaries of all persons employed by a large university. - The amount of time spent by students on a difficult exam. + *The amount of time spent by students on a difficult exam. - The grade distribution on a difficult exam. + *The grade distribution on a difficult exam. - + - + - ===Model Validation=== + - Checking/affirming underlying assumptions. + - + - * TBD + - + - ===Computational Resources: Internet-based SOCR Tools=== + - * TBD + - + - ===Examples=== + - Computer simulations and real observed data. + - + - * TBD + ===Hands-on activities=== ===Hands-on activities=== - Step-by-step practice problems. + * [[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]] - * TBD + -
+ ===[[EBook_Problems_EDA_Shape | Problems]]=== - ===References=== + - * TBD +

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

### 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.