Mean and median: Virtual manipulative
Introduction: Open the applet, http://illuminations.nctm.org/ActivityDetail.aspx?ID=160 and read through the instructions before you begin.
Practice together
1. Plot any 2 points. What do you notice about the mean and median? Do you think this is always true for 2 points?
2. Plot any 3 points and drag one or more of them around until the median is 15. What are the 3 points? Will everyone have some of the same data values? Why or why not?
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Problems:
For these next problems, plot 7 data values.
List your initial seven values here: ______
Initial mean: ______Initial median: ______
1. Can you find ways to move the data points that keep the median the same but change the mean? Explain. List the data set (if possible).
2. Can you find ways to move the data points that keep the mean the same but change the median? List the data set (if possible).
3. How do the mean and median change when you keep the points in the same order 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 in which the mean seems to be a typical value but the median is not? Give an example if possible.
6. By moving data points, can you construct data sets in which the median seems to be a typical value but the mean is not? Give an example if possible.
7. What sorts of changes in a data set make the mean change?
8. What sorts of changes in a data set make the median change?
9. Find examples in the popular press where the mean of a data set is cited and other examples where the median is cited. Why do you think the authors of those articles chose to cite those particular measures of center? Would readers have received a different impression of the data under discussion if other (or additional) measures of center had been reported? Send me the URL or the data sets.
Reading:
Read through the article, Developing a Meaningful Understanding of the Mean and then reevaluate your work on the questions above.
Reflection:
After you have worked through the problems, fill out the applet rubric. Also answer the following:
1. How did your prior knowledge about the mean and median affect the way you used the manipulative?
2. Would you want to do the above problems by “hand” without the use of technology? Explain.
More for the classroom
Other applets/activities/readings that might help you work with the mean and median in the classroom:
1. http://standards.nctm.org/document/eexamples/chap6/6.6/index.htm
2. http://www.shodor.org/interactivate/discussions/meanmedianandmode/
3. http://nlvm.usu.edu/en/NAV/frames_asid_200_g_4_t_5.html?open=instructions&from=category_g_4_t_5.html
4. http://www.shodor.org/interactivate/activities/Measures/?version=1.6.0_06&browser=MSIE&vendor=Sun_Microsystems_Inc.