The Advanced Placement (AP) exams are given to thousands of high school students every spring. The exams are graded on a scale of 1 to 5. A grade of 3 or better usually will be sufficient to obtain college credit for that course. Let’s take a statistical look at some of the results of last year’s test-takers.

A mathematics or statistics class.

Students should be familiar with Internet searching, know how to calculate percents and how to make bar charts. If this lesson is used in a statistics class, students should know how to perform a chi-square test.

Use the Internet to access current AP data.

Calculate and compare percents.

Construct bar charts.

Discuss whether the distribution of scores for different AP subjects seem to be significantly different.

Determine statistically whether these distributions are significantly different by performing a chi-square test.

Internet access. Calculator, spreadsheet or computer package that can create graphs and run a chi-square test recommended.

Students will access the College Board web site to obtain the data they need. They may then complete the AP Scores Worksheet either "by hand" or using calculator or computer.

See points on the worksheet. Students may be asked to report orally on their results. If students have been assigned different AP subjects to research, they may work in groups to display a table and graph showing their combined results.

Students may choose more AP subjects to compare and display a poster of their results for extra credit. They may look at SAT scores and compare Wisconsin scores with national scores.

!!!! 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.

Students could be assigned different subjects for comparison. After the students obtain the data they need from the Internet, they may complete the worksheet as an assignment either in class or outside of class. If students are not acquainted with the chi-square test, Question #8 should be omitted.

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. (10 points) Access the site http://www.collegeboard.org In the "Search for:" box, type Distribution of Grades. Click on AP Subjects and ENTER. Complete the following table. The AP site gives the distribution by percent. You will need to calculate the Number of Students in each score category.

Total number of students taking the statistics exam: _________________

2. (10 points) Find AP results for the Calculus exam.

Total number of students taking the calculus exam: _________________

3. (10 points) Choose another AP subject and find its test results.

Subject: ___________________

Total number of students taking the exam: _________________

4. (5 points) Do the distribution of scores seem different for the three subjects above? Explain your answer.

5. (5 points) Another way of comparing distributions is to make a bar chart showing the results of all three exams on one chart. Is it better to make the bar chart using the percent values or the number of students? Explain why.

6. (10 points) Make a bar chart showing the results of all three exams. Label the x-axis from 1 through 5. Use a different colored bar for each subject.

7. (5 points) Use the bar chart above to visually compare the three score distributions. Explain what you observe.

8. (10 points) Perform a chi-square test to determine if the distribution of scores for the three subjects are significantly different. State your null hypothesis, your alternative hypothesis and find the p-value for the chi-square test. Then state your conclusion.

9. (5 points) Which of the three AP exams seems to be the "easiest"? Which is the "hardest". Explain your answer.

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1. (10 points) Access the site http://www.collegeboard.org In the "Search for:" box, type Distribution of Grades. Click on AP Subjects and ENTER. Complete the following table. The AP site gives the distribution by percent. You will need to calculate the Number of Students in each score category.

Total number of students taking the statistics exam: 15,486

2. (10 points) Find AP results for the Calculus exam.

Total number of students taking the calculus exam: 117,671

3. (10 points) Choose another AP subject and find its test results.

Subject: Physics B

Total number of students taking the exam: 24,276

4. (5 points) Do the distribution of scores seem different for the three subjects above? Explain your answer.

The percents for the Statistics and Calculus exams seemed somewhat similar to one another, but different from the Physics percents.

5. (5 points) Another way of comparing distributions is to make a bar chart showing the results of all three exams on one chart. Is it better to make the bar chart using the percent values or the number of students? Explain why.

Percent values, since these percents are comparable no matter how many students took each exam.

6. (10 points) Make a bar chart showing the results of all three exams.

7. (5 points) Use the bar chart above to visually compare the three score distributions. Explain what you observe.

It seems there is a higher percentage of score 3 for Physics and lower of scores 2 and 4 for Physics as compared to both Statistics and Calculus. More Physics students were "average".

8. (10 points) Perform a chi-square test to determine if the distribution of scores for the three subjects are significantly different. State your null and alternative hypotheses, the p-value and your conclusion.

H₀: The percentage distributions are the same for the three tests.

H_A: The percentage distributions are not the same for at least some of the three tests.

The p-value for the chi-square test is almost 0, or 2.64 E-194 = 2.64 X 10 ^-194

Hence we reject H₀ and conclude that the percentage distributions for at least two of these three tests are statistically different.

9. (5 points) Which of the three AP exams seems to be the "easiest"? Which is the "hardest". Explain your answer.

Combine score categories 5 with 4 and 1 with 2. Then the percentages are:

It seems Calculus was the "easiest" because it had the highest percent in the 5,4 categories and almost the lowest percent in the 2,1 categories. It seems Statistics was the "hardest" since it had the highest percent in the 2,1 category and almost the lowest percent in the 5,4 category.