Data Management and Analysis:
Secondary Level Ideas

by
Jeff Walters,
Estevan Comprehensive School,

 Subject: Math B30 Section B - Data Analysis Topic: Standard Deviation Using the Internet Objectives: The student will learn about standard deviation by visiting different Internet sites while making notes on what they are finding. The student will learn to calculate the standard deviation of a set of data using a calculator or by hand. Materials Needed: Internet access, Web browser, Calculator Teacher Notes: This lesson will cover a portion of objectives B2 and B3 from the Saskatchewan Education B30 curriculum guide. It will probably require more than an hour if your class (and you!) are new at using the Internet. It is assumed that a student understands the concept of a normal distribution. Most sources say that normal distribution is described as having 99.7% of the data occur within three standard deviations of the mean. The bell curve is symmetrical about its mean. Other sources say that the mean is equal to the median in a normal distribution.

A. Introduction to Standard Deviation

Make sure students are prepared to answer questions at the end of this unit by having them take notes on the following sites that develop the concept of standard deviation.
Have students log on to the Internet and type in the following web address in their web browser. http://www.cs.rice.edu/~bchristo/lessons/sta ndev/ Students should work through all five parts to this self-directed tutorial.

The five sections are:
1. An Introduction
2. Why We Need It
3. Calculating It & Understanding It
4. Using It in the Real World
5. Resources

Teacher Note:
The creator of the above tutorial, Barb Christopher has also written two lessons about standard deviation that can be found at http://www.cs.rice.edu/~bchristo/lessons/Sta nDev1.html and http://www.cs.rice.edu/ ~bchristo/lessons/StanDev2.html that may be useful. In addition to this tutorial, the students should look at the following sites for additional information about standard deviation. If the above link isn't complete yet, start at http:// nilesonline.com/stats/stdev.html This section is from an online guide called Statistics Every Writer Should Knowand is very practical for student use because it gives a down-to-earth description of standard deviation. It is written for journalists but is easily transferrable to students.

B. The Math Behind Standard Deviation

Next onto how the standard deviation formula is useful.
Have students go to Math Central (U of R math web site) at http://mathcentral.uregina.ca/RR/ database/RR.09.95/weston2.html Here they will find "A Note on Standard Deviation" by Harley Weston. This is an excellent explanation of how the standard deviation formulas are obtained. Plus Harley describes the difference in the statistical standard deviations (n-1) and the population standard deviation (n). The curriculum guide points out that both are useful but for the B30 course, we are to use the standard deviation for a population.
For the more advanced students, another explanation for the standard deviation formula may be obtained from http://forum.swarthmore.edu/dr.math/proble ms/morris20.html The following two questions are posed to Dr. Math of Swarthmore University about standard deviation. Possible Questions: Explain why one needs standard deviation. Briefly explain to your partner how the standard deviation formula is found. Why are there two standard deviation formulas and when is it appropriate to use sample or population standard deviation formulas?

C. Calculating Standard Deviation

Now that the students understand the concept of standard deviation, they should begin calculating it. I will provide some sites with data that you can use to find standard deviation but leave the actual calculations up to you. You may want to do a few examples using tables and charts to find standard deviation by hand. When using the calculator, each student will need some time to become comfortable with how their calculator changes modes and calculates the different statistical calculations. If you have TI-82 calculator, the LIST option is very handy for entering data, sorting it and finding the many variance statistics all at once.
 1 The following is a site from the Minnesota Attorney General's Office about fast food. Under the question, "Which restaurant do you want to search?" Choose DOMINO'S PIZZA from the pull down menu and then press FIRE UP THE DEEP FRYER. Have the students calculate the standard deviation for the fat content of the different Domino's pizzas. Since there are only 12 entries, it is a good first attempt at finding standard deviation. I also believe this is a normal distribution so they could practice drawing the normal curve.   Questions: Is this a normal distribution? Draw the distribution with the appropriate percentages. Repeat the above for Pizza Hut's Pizzas. Compare the standard deviations. Why are they different? How could you explain this difference?   Teacher Note: They could practice finding standard deviations for any of the other headings. This is a good site to come back to when talking about z scores and comparing data from different distributions. 2 At Statistics Canada a table called, Births and Birth Rate, Canada, the Provinces and Territories can be found at http://WWW.StatCan .CA/english/Pgdb/People/Population/demo04a. htm Have the students use the numbers for Canada expressed as birth rate per 1000 people, which are at the bottom of the page. This appears to be normally distibuted.   Questions: Predict if the standard deviation will be smaller or larger for Saskatchwan. Find the standard deviation using the Sask Birth Rates. Where you correct? Why or why not? 3 A weather site to compare data can be found at the following location. http://WWW.StatCan.CA/english/Pgdb/Land/G eography/phys08a.htm The table, Weather Conditions in Capital and Major Cities can be used to find the standard deviations of average snowfall, precipitation, etc.   http://WWW.StatCan.CA/english/Pgdb/Land/G eography/phys08b.htm gives a table called "The average annual temps."   This should give the students a good start in understanding standard deviation and how to calculate it. You may also want to watch whether or not data is normally distributed and have students investigate some data further. I know we don't all have classroom Internet access, myself included, but at least this may help people that do use the Internet in their classes. Most people have Internet access of some type so you can use this to obtain data, research the concept and organize it however you see fit.

Wanting a link to more sites on statistics? Try the following.

US Based Stats but well organized. http://nilesonline.com/data/links.shtml