AP Statistics Curriculum 2007 EDA Shape

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* 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 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:
* '''Multimodal''' distributions have two or more than one 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]

Revision as of 02:19, 28 January 2008

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

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




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