One of the first things taught in the study of Statistics is how to display data. Lists of numbers are often meaningless to many people. A visual representation, however, can show many important features of the data at a glance. In this lesson, students will access salary statistics on the Internet for various occupations and select the most appropriate graph to answer particular questions about their data.

Any mathematics class. Any business or economics class studying different occupations.

Students should be able to locate a given Internet site. They should be acquainted with various types of graphs, such as histograms, pie charts, boxplots, scatterplots, line graphs, dot plots, etc.

To use the Internet to find current salary data for various occupations.

To display a given set of data with an appropriate graph.

To use graphs to study trends and predict future outcomes.

Students will access the National Center for Education Statistics web site, find a particular data table and display a graph to emphasize certain aspects of the data. They should follow the directions on the Salary Statistics Activity Sheet.

See points on the Activity Sheet. If time permits, a short oral class presentation or a "poster presentation" may be required or completed for extra credit. Points for such a presentation should be based on:

1. Correctness and neatness of graphs.

2. Appropriateness of graphs used to emphasize the desired aspect of the data.

3. Clear explanations of why that particular graph was chosen and how the graph was constructed from the data.

Internet access. Graphing calculator or graphing software may be used.

The web site students will be using has many data tables. Students could pick another data table to use and make a graph to show a particular aspect of that data. If statistics software is available, students may find "best-fit curves" and then use the equations to make predictions. Students may search the web for some unusual types of graphs and explain to the class how they are constructed and why they are used.

!!!! Warning !!!! The Web sites given in this lesson may have changed! Before using this lesson with your students, be sure to check if the sites are still working or if you must find another site. Sometimes the sites still have the relevant data but you may need to change the directions to access the data.

The instructor may review various types of graphs, such as pie chart, bar chart, dot chart, line graph, histogram, box-and-whisker graph, scatter diagram, before assigning this activity. A good site for examples of these graphs is http://www.eia.doe.gov/neic/graphs/introduc.htm The site http://www.yorku.ca/SCS/Gallery shows the "best and worst of statistical graphs."

If you wish more background about the statistical concepts involved in the lesson, some good sites to check are:

http://davidmlane.com/hyperstat/index.html

http://www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html

http://www.math.unb.ca/~maureen/SSCEdCom/basicstats/basicstats.html

http://www.math.unb.ca/~knight/BasicStat/$content.htm

http://www.bbns.org/us/math/ap_stats

http://www.grad.cgs.edu/wise/linksf.shtml

http://www.cvgs.k12.va.us/DIGSTATS

http://www.statsoft.com/textbook/stathome.html

http://www.stats.gla.ac.uk/steps/glossary/index.html

http://www.crpc.rice.edu/CRPC/GT/sboone/Lessons/lptitle.html

http://forum.swarthmore.edu/library/topics/statistics

http://www.psychstat.smsu.edu/introbook/skb00.htm

TI-83 instructions:

http://www.ti.com/calc/docs/act/koehler001.htm

http://www.wku.edu/~neal/manual/ti83.html

The Calculator website at the Mathematics Department of the University of Wisconsin-La Crosse will perform basic statistical calculations. If you do not have access to a simple statistical computer package or calculators with statistics options, your students may access http://www.compute.uwlax.edu/stats_htdocs/newmenu.html to perform statistical computations on-line.

In order to print out just a copy of the student worksheet, highlight this section, then copy and paste it into your word processor. You may then revise the worksheet if you wish.

1. (5 points) Access the site http://NCES.ed.gov Then click on National Center for Education Statistics (NCES) or on the Encyclopedia of Educational Statistics, then on The Digest of Education Statistics, and finally on Lists of Tables. Use Table 394 "Average annual salary of bachelor's degree recipients employed full-time 1 year after graduation". (This site updates their web site regularly. If Table 394 does not give the correct information, use the search option to find the correct table.)

2. (12 points) Describe three different kinds of graphs you might make to illustrate some information from this table.

3. (10 points) Make an appropriate graph to show what the salaries in all fields were in 1989-90. What fields have the highest salaries? Which had the lowest? Would this still be true today? Explain why or why not.

4. (10 points) Make an appropriate graph to show how salaries in the Humanities, Business and Engineering have changed from 1976 to 1994. Which professions are "better off" in 1994 than in 1976? Explain why.

5. (10 points) Make a graph to show which professions had "real" increases in salary from 1974 to 1994.

6. (10 points) Make a graph to illustrate some other information from this table. Explain why you chose this type of graph.

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1. (5 points) Access the site http://NCES.ed.gov Then click on National Center for Education Statistics (NCES), then on The Digest of Education Statistics, and finally on Lists of Tables. Use Table 394 "Average annual salary of bachelor's degree recipients employed full-time 1 year after graduation". (This site updates their web site regularly. If Table 394 does not give the correct information, use the search option to find the correct table.)

2. (12 points) Describe three different kinds of graphs you might make to illustrate some information from this table.

Box plot to summarize all salaries during one year.

Paired bar chart showing both 1976 and 1994 salaries for all profession.

Line graph showing the percent change in constant dollars from 1987 to 1994.

Scatterplot of current 1976 dollars versus 1994 dollars.

Dot plot showing all salaries during one year.

3. (10 points) Make an appropriate graph to show what the salaries in all fields were in 1989-90. Which fields had the highest salaries? Which had the lowest? Would this still be true today? Explain why or why not.

 Highest salaries: science and health professions

Lowest salaries: education, humanities, psychology

The science and health professions would probably still be high today because of the scientific training needed. Perhaps education may be higher today because there is beginning to be a shortage of teachers. (Supply and Demand)

4. (10 points) Make a graph to show how salaries in the Humanities, Business and Engineering have changed from 1976 to 1994. Which professions are "better off" in 1994 than in 1976?

Engineers gained, then lost "real" salary. Their salary in 1994 is comparable to their 1976 salary. Business salaries remained constant. However humanities had a "real" gain from 1976 to 1981 and kept this gain. Hence the only profession that is "better off" is the humanities.

5. (10 points) Make a graph to show which professions had real increases in salary from 1974 to 1994.

A. Education

B. Mathematics

C. Humanities

D. Social Science

E. Miscellaneous

F. Biological Sciences

G. Business/Management

H. Health

I. Engineering

The higher a point is above the line, the greater the real salary increase. The Health professions (H) saw the greatest real salary change; the engineering profession (I) saw a slight decrease.

6. (10 points) Make a graph to illustrate some other information from this table. Explain why you chose this type of graph