Measures of Central Tendency Task
(adapted from NCTM e-example)
The seven data points in the line plot represent the distances a paper airplane
traveled after it was thrown. Your task is to explore how changing one (or
more) of the data points affects the mean and the median of the data set.
Open Interactive Line Plot
http://standards.nctm.org/document/eexamples/chap6/6.6/standalone1.htm
Use the following questions to focus your experimentation:
1. Can you find ways to move the data points that keep
the median the same, but change the mean? If so, how? If not, why not?
2. Can you find ways to move the data points that keep
the mean the same, but change the median? If so, how? If not, why not?
3. How do the mean and median change when you keep the
points in the same order (1st, 2nd, 3rd, etc), but just change their positions
on the number line?
4. What happens if you pull some of the data values way
off to one extreme or the other extreme?
5. By moving data points, can you construct data sets where
the mean seems to be a typical value, but the median is not? Vice versa?
6. For what types of data sets, if any, is the mean not
very representative? When is the median not very representative?
IF TIME: Open the following website
http://www.explorelearning.com/math/MeanMedianMode/
How could this interactive tool be used to help students conceptualize mean,
median, and mode? What properties of the mean and median are highlighted
with this applet? Are there any advantages or disadvantages to the metaphors
used in this tool?