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QIWCourseware by Dan DuPort

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- 1. An example of interactive technology enhanced learning. Interacting with a changing data set to learn about standard deviation.
- 2. How would you tell someone about standard deviation (SD)? • The following (4 slides) illustrates how a beginning statistics student has interactions with the concepts. They are guided thru an understanding of concepts by visualization of parameter changes as they interact with the data set. • While the mean of a data set is fairly easy to understand, the SD is often not understood until a student has studied statistics for a while. The formula for SD is often a stumbling block, and another is that it varies in a complex manner when the data changes -- because then the mean varies. Sure, you can say it represents the averages of the distances of the data points from the mean. But how do you get a feel for it.
- 3. Here’s a way the students can get a hands on feel for SD. We start with a simple uniform distribution, 10 has frequency 1, and 20 has frequency 1. And note that everything is intuitive. The mean is 15, and the SD is 5.
- 4. Now change the frequency of 20 to 2. We see the mean move towards 20 as one more piece of data of value 20 is added to the data set. The mean becomes 16.67, closer to 20. So the SD becomes smaller, 4.71, because there are more points closer to the mean than before.
- 5. Now, let’s check that the SD is more intuitive if we add another point of value 10. We’re not disappointed.
- 6. Let’s see what happens with a lot more points of value 20. We’ll add 7 points. As suspected, the mean is dragged very close to 20, and the SD gets considerably smaller, with value 3.86, because of the large number of points that are close to the mean.
- 7. The Big Idea is that people learn from doing the interaction, not just seeing it! Download a copy of STEMLi from QIWCourseware.com Do some interactions and see what I mean. Use it for free, no strings attached, for learning the basics of statistics. 44 pages of interactive, visual learning that’s easy on the mind. Requires Excel 2010 for the PC Excel 2011 for the MAC or higher

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