Sunflower+MAD

=Sunflower Height MAD and the Average Deviation Hat Plot= Developed: Summer 2012 Posted: 1/31/13 Return to Mean Absolute Deviation Background: The heights of sunflower plants can range from 12 inches to 15 feet. The height depends on the variety, season, USDA plant zone, amount of water and how closely the seeds are planted to each other.

This data set contains the heights for 10 plants. The problem was intended for a "by-hand" calculation with the use of a calculator. On this wiki page, I will introduce the **-1.00 to +1.00 Average Deviation Hat Plot** (in the hats plot menu). **This type of hat plot is quite different from the percentile range plot or box plot.** While the MAD is the stepping stone to the Standard Deviation, the -1.00 to +1.00 Average Deviation Hat Plot is the stepping stone to the Standard Normal Distribution (see the third graphic below).
 * Sunflower Collection 1**

- raw data - completed work The table and the plots for this set of sunflower data indicate a MAD of 11 inches. Note that the Average Deviation Hat Plot of plant height marks the lower crown of the hat at 89 - 11 = 78 inches and the upper crown at 89 + 11 = 100 inches. I used three vertical dividers to show these values on the hat plot.

The ** population standard deviation ** for this data set is approximately 11.8 inches. By adding the hat plot and measuring from the mean to the right crown, I can "see" the standard deviation value in the plot. Note that I use this feature and technique to teach the Central Limit Theorem (yes, with TinkerPlots). Note that TinkerPlots has the advanced statistical functions found in Fathom Dynamic Data Software.

This data set contains the heights for 12 plants. The problem was not used for a "by-hand" calculation. The problem was used to test students ability to sketch an average deviation hat plot. This provides an example of how I used TinkerPlots to create problems. A jpeg of the file's contents is shown below. - raw data - completed work
 * Sunflower Collection 2**

This last data set is pretty nasty due to the eleven plants. I would use this if technology was available (statistics feature on a graphing calculator, spreadsheet or TinkerPlots). My goal is that students understand where the numbers come from and what they represent.
 * Sunflower Collection 3**

- raw data - completed work

Please let me know if you have any questions or comments regarding the content of this page. Kathy