This document describes an interactive approach to teaching standard deviation using a changing dataset. Students can visualize how changing the data values affects the mean and standard deviation. They start with a simple uniform distribution and see that increasing the frequency of one value drags the mean closer to that value and decreases the standard deviation as more points are closer to the new mean. The interactive experience helps students build intuition for standard deviation rather than just seeing explanations.

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