Tuesday, December 6, 2016

Statistics on the Results of the 2016 Advanced Placement Exams

Statistics on the Results of the 2016 Advanced Placement Exams

The questions in this blog involve different statistics on the grades of 20 Advanced Placement exams.

What are the average, median and mode grade for each AP exam and all AP exams?

What does each statistic tell us about performance on AP exams?  How does information from these statistics differ?

In your view should policy makers focus more on procedures and programs designed to improve exam performance or increasing participation on the test?

I discuss the need for more statistical work that will attempt to determine what factors lead students to succeed or fail on these exams.   I conclude with my views on policies, which might improve performance on AP exams?


The Data:  The data below on grades received in AP exams in 2016 was obtained from College Board web sites.

There are several such web sites.  Data is available in either an Excel file or a PDF at the web site below.




Advanced Placement Exam Results (Number of Grades Received 2016
Test/Grades
5
4
3
2
1
Total
United States History
58,338
87,745
110,297
113,885
119,026
489,291
World History
18,953
44,424
83,774
81,877
56,323
285,351
Spanish Language   (Total Group)
43,174
53,845
41,801
14,302
2,136
155,258
Statistics
29,627
44,884
51,367
32,120
48,565
206,563
Psychology
55,977
76,418
55,937
41,566
63,452
293,350
Physics C Mechanics
17,163
14,357
9,590
6,971
5,029
53,110
Physics 1
7,746
23,770
35,840
51,092
50,856
169,304
Government & Politics  United States
36,449
40,068
73,796
71,074
74,721
296,108
Human Geography
22,054
37,103
36,531
35,360
53,615
184,663
English Literature
30,137
72,163
119,194
135,355
48,597
405,446
Environmental Science
11,350
34,627
21,999
38,474
42,646
149,096
European History
8,025
17,461
31,828
38,324
13,393
109,031
Computer Science A
12,055
11,900
13,386
7,215
13,381
57,937
Economics - Macro
23,471
31,546
21,733
22,902
34,986
134,638
Economics - Micro
14,632
22,691
18,153
11,270
15,642
82,388
English Language
58,398
96,168
148,574
175,579
68,856
547,575
Biology
15,661
49,944
79,947
68,494
24,034
238,080
Calculus AB
76,486
53,467
53,533
30,017
94,712
308,215
Calculus BC
60,632
19,191
21,441
7,212
16,455
124,931
Chemistry
16,166
23,913
42,202
37,994
33,190
153,465
616,499
855,689
1,070,926
1,021,085
879,616
4,443,800
Results of AP exams taken by at least 50,000 people in 2016


Answers:  In order to calculate the mean, median, mode and standard deviation of grades for the 20 exams we need the likelihood of each grade for each test.  These probabilities are presented below.


Grade Likelihoods for Each AP Exam in 2016
Test/Grades
5
4
3
2
1
Total
United States History
0.12
0.18
0.23
0.23
0.24
1.0
World History
0.07
0.16
0.29
0.29
0.20
1.0
Spanish Language   (Total Group)
0.28
0.35
0.27
0.09
0.01
1.0
Statistics
0.14
0.22
0.25
0.16
0.24
1.0
Psychology
0.19
0.26
0.19
0.14
0.22
1.0
Physics C Mechanics
0.32
0.27
0.18
0.13
0.09
1.0
Physics 1
0.05
0.14
0.21
0.30
0.30
1.0
Government & Politics  United States
0.12
0.14
0.25
0.24
0.25
1.0
Human Geography
0.12
0.20
0.20
0.19
0.29
1.0
English Literature
0.07
0.18
0.29
0.33
0.12
1.0
Environmental Science
0.08
0.23
0.15
0.26
0.29
1.0
European History
0.07
0.16
0.29
0.35
0.12
1.0
Computer Science A
0.21
0.21
0.23
0.12
0.23
1.0
Economics - Macro
0.17
0.23
0.16
0.17
0.26
1.0
Economics - Micro
0.18
0.28
0.22
0.14
0.19
1.0
English Language
0.11
0.18
0.27
0.32
0.13
1.0
Biology
0.07
0.21
0.34
0.29
0.10
1.0
Calculus AB
0.25
0.17
0.17
0.10
0.31
1.0
Calculus BC
0.49
0.15
0.17
0.06
0.13
1.0
Chemistry
0.11
0.16
0.27
0.25
0.22
1.0
Total
0.14
0.19
0.24
0.23
0.20
1.0


The average grade for each of the 20 AP exams is presented below.



Average Grade on AP Exam
Expected Grade
United States History
2.70
World History
2.61
Spanish Language   (Total Group)
3.78
Statistics
2.88
Psychology
3.07
Physics C Mechanics
3.60
Physics 1
2.33
Government & Politics  United States
2.64
Human Geography
2.67
English Literature
2.75
Environmental Science
2.55
European History
2.71
Computer Science A
3.04
Economics - Macro
2.89
Economics - Micro
3.11
English Language
2.82
Biology
2.85
Calculus AB
2.96
Calculus BC
3.80
Chemistry
2.69
Total
2.84


Comments on the average grades for the 20 tests:

I calculated the average by taking the SUMPRODUCT of the grades with the corresponding percent of students getting each grade

The average grade is less than a C for 14 of the 20 exams.

The average grade for the total of all tests taken is 2.84 also below a C.

Comments on the median:

The median grade is the lowest grade where 50% or more of the people have grades less than the median.

I found the median through a repetitive process involving logical statements.  I will soon write a math post showing this procedure.

Start with a grade of 1 and flag all tests where 50% of students had a grade of 1 or less.    

There were no such tests.

Go to grade of 2 and flag all people where 50% of students had a grade of 2 or less.  

There were two such tests, AP Environmental Science and AP Physics 1.

Go to a grade of 3 and flag all tests that were not flagged at grade of 2 and where 50% of people had a grade of 3 or less.   There were 15 such tests.

Go to a grade of 4 and flag all tests that were not previously flagged and where 50% of students had a grade of 4 or less.   There were 3 such tests, Calculus BC, Physics C Mechanics, and Spanish.

The median grade for all tests taken was a C.

Comments on the mode:

The mode is the category with the highest number of observations.   The mode grade can be found by putting MAX functions inside if statements. 

There are two exams with mode grade A, 3 exams with a mode grade of B, 5 exams with a mode grade of C, 4 exams with a mode grade of D, and 6 exams with a mode grade of F.

It is quite disconcerting that the mode of the modes is an F.   More exams had a mode grade of F than a mode of some other grade.

The overall mode grade over all tests taken was a C.   The proportion of overall tests with a C was only slightly higher than the proportion of overall tests with a D>

Concluding Remarks:  If you want to paint a favorable view of AP exam performance look at median grades for the 20 exams. If you want to paint a negative view look at average grades and mode grades for the 20 exams.

An additional statistic involves comparing the percent of people with a D or F to the number of people with an A or B on each exam.  On 13 of the 20 exams the likelihood of a D or F on an AP exam exceeded the likelihood of an A or B.

These numbers suggest to me that a lot of students are wasting their time on AP exams and the emphasis should be on procedures and programs that increase performance rather than increased participation.

This is a really interesting problem and I am in the process of writing research proposals that will help us better understand the factors impacting performance on AP exams and help in the development of policies and procedures that could improve student performance.  

Authors Note:  Some of my most important work right now involves health care and the likelihood that the Affordable Care Act will be repealed and replaced.   I have several questions and concerns about Trump’s replacement plan that are listed in the post linked below.








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