Difference between revisions of "AP Statistics Curriculum 2007 EDA Shape"
(→Definitions) |
m (Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/") |
||
| (One intermediate revision by one other user not shown) | |||
| Line 9: | Line 9: | ||
*** 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 modes. Examples of multimodal distributions are: | * '''Multimodal''' distributions have two or more modes. Examples of multimodal distributions are: | ||
| Line 39: | Line 40: | ||
* SOCR Home page: http://www.socr.ucla.edu | * SOCR Home page: http://www.socr.ucla.edu | ||
| − | {{translate|pageName=http://wiki. | + | "{{translate|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_EDA_Shape}} |
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
"-----
Translate this page:
