# AP Statistics Curriculum 2007 EDA Shape

(Difference between revisions)
 Revision as of 01:08, 28 January 2008 (view source)IvoDinov (Talk | contribs)← Older edit Revision as of 02:21, 28 January 2008 (view source)IvoDinov (Talk | contribs) Newer edit → 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 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]

## 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
• Multimodal distributions have two or more than one 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.