# ACT Scores: What Do They Really Mean?

Recently overheard in an airport, “I am a really smart kid. I scored a 27 on my ACT, which is near perfect. But my grades were pretty bad, because I didn’t apply myself well enough. Think of me as an A student who got C’s.”

It’s the common thing I heard as a faculty member at universities in Wisconsin and Maryland. Students would tell me that they didn’t deserve a ‘C’ grade despite scoring a seventy-two percent overall for the course and then would back it up with a relatively similar quote about being a good student, or an A student, or one of the hardest-workers; and they all fell on bad times. I rarely treated them harshly, but would have to evaluate each situation on their own and decide a method for aiding the student out.

## Quality of Student: Sum-Total, Not Total Sum

For example, over a decade ago one student finished my introduction to algebra course at UW-Milwaukee with a 68% and I had rolled it into a C grade. The student told me about the passing of their father earlier in the semester; which jived with the grading curve. The student brought in materials to prove their father’s passing, and I managed to convince the department to give the student an extension to the course that led into the first six weeks of summer. The student worked hard and finished the course with a 77%; which led to me passing him with a B grade.

On the other end of the spectrum, a student scored a 71%, and I gave them a C score. They talked to me after class, telling me that my class was the hardest math class (introduction to statistics) they had ever taken and it was unfair to not round grades up a full letter. I showed the distribution of the class scores to the student; which of the 118 students, they fell in the bottom 15 students. The class average was 89%. The student asked for an extension to make up work. After some discussion, I agreed to give the student two weeks to retake a two week section of the course (one they had bombed) with the offer to tutor one hour a day for each of the five days that week. The student accepted and promptly skipped all tutoring sessions, did not turn in the two homework assignments, arrived to take the exam and scored just as poorly as the first time.

In short between these examples, it became quite clear that scores rarely reflect the quality of student and their ability to excel in a classroom setting. Instead it was the student’s abilities to navigate a course through the ups-and-downs of life; between struggling to keep up with demands of continuous coursework and the possible anxiety of taking exams. Through 13 years of teaching at the collegiate level from introductory levels of college through masters courses, I have definitely seen a wide range of students. I’ve seen students who destroy exams and do little coursework, students who get destroyed by exams but master the coursework, students who are so good they would have made me look like a clown in the same class, and students who just “straight don’t give a damn” as my fourth grade teacher, Mr. Harris, would say.

So when I gave out my grades, I looked at not only their total sum of points, but I also looked at their sum-total of efforts and external factors. I’ve always followed the lower limits of a course syllabus, but would always promote students’ efforts over the upper limits. For instance, in the previous story, I gave a student a letter grade higher despite not hitting the required limit (minimum 80% for a B) in due part that I knew the student went through hard times and still nailed close to 80% of the material. I have done the same for strong finishers, the students who struggle in the beginning but catch on midway through class and hammer out high grades at the end. In fact, my typical class policy is: If you score a 95 or higher on the cumulative final; you get an A. No questions asked. In the history of teaching my courses; through a couple thousand students, I have given out close to 20 A’s with students who have scored less than 85% (Only two below 80%: 79%, 77%). However, if a “lazy” student hit 81% and I thought the student deserved a “C”; the student was given their “B”. That was the contract and they earned their right to the B-grade.

So why go into a lengthy diatribe about what grades students earn? Simple. Because grades are given out like medals at a marathon. Everyone gets one and everyone is ranked at the end. In marathons, it’s times and the feeling of accomplishment (or lack there of if a bad run). In courses, it’s grades. But the sum-total of completing both gets reflected in the rating system at the end. Grades are not rigid; despite exam scores being so. And that’s what leads us into standardized testing.

## ACT: One Test to Benchmark All

The ACT exam started in 1959 at the University of Iowa and was designed as an alternative examination to the SAT. Everett Franklin Lindquist developed the test to include a science assessment, with a focus on college readiness. The exam became wildly popular and since its inception 57 years ago, is taken by 1.8 million people worldwide per year.

The test is similar to the SAT in effect to provide a benchmark for all students in an attempt to identify “college readiness.” However, the test (as noted above at the start of this article) is notably misinterpreted as the quality of student. For instance, a high ACT score does not indicate the student is truly ready for college; nor does it determine if the student is an “A” student. Similarly, a low ACT score does not indicate that a student is not truly ready for college; nor does it indicate the student is a “F” student.

In a recent posting, the Chief Executive Officer (Marten Roorda) stated that while their exams cover areas such as Algebra II (intermediate algebra) and Trigonometry, only 84 percent of “high majority” schools and 71 percent of “high minority” schools offer Algebra II at a minimum. Thus, a baselining exam is set slightly higher than the basic admissions of majority of universities (Algebra II is the typical requirement; a level lower than trigonometry) and at a level higher than over 15% of high schools in the United States. In a double edged-commentary; this highlights that usual ACT exam as not being a benchmark to compare students from schools (as it tests above the level of roughly a sixth of the nation’s high schools and above standard college requirements). But it also highlights, ACT’s commitment to life-long learning and improving STEM across the country at all ages.

## ACT: Scoring

Now we take a look at the scoring for the ACT. The exam is broken into four parts: English, Mathematics, Reading, and Science. The English section is a series of 75 questions taken over a 45 minute span. The math section comprises of 60 questions over a 60 minute span. The reading section contains 40 questions over a 35 minute portion. Similar to the reading section, the Science section is a series of 40 questions over 35 minutes. Each section maps a series of points into a score between 1 and 36 for each section. The scoring for each section maps to the following 1-36 points:

 Score English Math Reading Science 36 75 59-60 40 40 35 73-74 57-58 39 39 34 71-72 55-56 38 38 33 70 54 37 32 69 53 37 31 68 52 36 36 30 67 50-51 35 35 29 66 49 34 34 28 64-65 47-48 33 33 27 62-63 45-46 32 31-32 26 60-61 43-44 31 30 25 58-59 41-42 30 28-29 24 56-57 38-40 29 26-27 23 53-55 36-37 27-28 24-25 22 51-52 34-35 26 23 21 48-50 33 25 21-22 20 45-47 31-32 23-24 19-20 19 42-44 29-30 22 17-18 18 40-41 27-28 20-21 16 17 38-39 24-26 19 14-15 16 35-37 19-23 18 13 15 33-34 15-16 16-17 12 14 30-32 12,13,14 14-15 11 13 29 10,11 13 10 12 27-28 8,9 11,12 9 11 25-26 6,7 9,10 8 10 23-24 5 8 7 9 20-22 4 7 6 8 17-19 6 5 7 14-16 3 5 4 6 11,12,13 4 3 5 9,10 2 3 4 6,7,8 2 3 5 1 2 1 2 3,4 1 1 0,1,2 0 0 0

What is not explicitly mentioned about the ACT is that questions are scored equally; indicating that questions about pre-algebra are equivalent to trigonometry. Thus, the standardized exam is really a weighted “point per question” exam on subjects that may or may not be available at your local high school. To remedy this, the ACT establishes “benchmarks” defined on their website.

## Benchmarks: 21 is the “Goal”

The defined benchmark lists (under the college readiness moniker) the score that will indicate a student has a “50% chance of obtaining a grade of ‘B'” and “about a 75% chance of obtaining a grade of ‘C'” in an equivalent college entry course. These scores are 18 for English, 22 for Mathematics, 22 in Reading, and 23 in Science. Hence the overall benchmark score is a 21. That is, (18+22+22+23)/4 = 85/4 = 21.25 -> 21.

By looking at college admissions at the Princeton Review, it is easy to see that the acceptance scores for most universities and colleges have approximate median values of 21 and 26 for the lower and upper quartile regions. For instance:

 School Lower 25% Upper 25% Carroll University 21 26 UMBC 24 28 College Park 25 29 Harvard 32 35 Stanford 31 35 CS Stanislaus 16 22 CS Fullerton 19 24 NM State 18 24 Illinois 26 32 UW Madison 27 31 UW Milwaukee 19 24

No compare to college GPA to the scores as we find that, in the case of UW-Milwaukee (the school I previously taught at), 46% of students have below a “B” average. That is, the school has 54% or higher of the student population at a “B” average or higher. Unless a quarter of the distribution of student ACT scores is squeezed all within the next two points (20 and 21), we should expect much less than the 46% of students having a B score or higher. Note: For a 46% average, we should expect roughly 92% of the school to score more than a 21 to obtain a 50% probability to hit the 46%. However, only 75% of the school scored higher than an ACT score of 19. Which means even less scored than 21 points.

UW-Milwaukee is considered close for matching benchmarks to ACT scores. Compare to schools such as Carroll University and Harvard; and things are not even close. The national average for ACT scores in 2015 was 20. This would indicate, based on the ideal definition of “C” student being average (center of the pack), a 20 would actually map to a C score. In college settings above, a score of 20 maps to between C (UW-Milwaukee) and A (Harvard College).

## ACT: Point Values As a Single Exam

So the exam doesn’t really treat all students and schools as equals and do not uniformly benchmark across all colleges that it aims to benchmark. Furthermore, the exam treats all questions within each subject as equal. So let’s get back to the exam itself and treat it for what it really is: a multiple choice exam with weighted scoring. It’s subjected to the same demons of standard comprehensive exams within a school; test anxiety, non-representation of student work ethic, and able to be prepped for as it is defined before the actual exam.

So let’s break down the exam as a graded exam. In this case, the exam is worth 215 points total that is re-weighted into a score of 36 points. For each of the 36 possible points, we can identify the upper and lower bounds for percentages of points scored.

For instance, for a perfect score, you do not need a perfect score. In fact, for a perfect score, all that is needed is a 36 score in all four sections. One wrong question in math still maps to a 26. Therefore it is possible to score either 214 out of 215 points; or 215 out of 215 points. Thus an ACT score of 36 maps to a score of 99.5349% to 100.0000%. Over the last few year, approximately 1100 of the 1.4 million students have scored a perfect score.

Continuing on with this exercise, we find that for a score of 35, the minimum score needed is 206, or a 95.8140%. The maximum for a 35 score is 214, or 99.5349%. What about the benchmark of 21? This maps to a point region of 86 points to 151 points. This maps to a range of 40.0000% to 70.2326%. This means that a 21 ranges from an F student to a C student. Hence the question becomes… what type of student does a 21 represent?

This comes back to the external factors. In fact, a college will state its “minimum requirements” in a fashion that states ranges and uses words such as typical; including exclusive schools such as UW-Madison. But 27 is not a minimum score. UW-Madison also advocates other scores such as class rank and GPA. They also consider rigor of the coursework, with a schedule of courses: 4 years English, 4 years Mathematics, 3-4 years Social Sciences, 3-4 years Sciences, 3-4 years Foreign Languages. And not only that, the school is also interested in external factors such as character, service, leadership, talents, citizenship, and interests.

Once you complete going through a standard school application process, you find out that the ACT score is merely a single parameter of many within overall application process. So in the end, the ACT score is a singular important test that helps maximize only a single parameter within the application process. Take for instance my lowly 3.25 GPA in high school; far below the 3.7 or higher academic restriction for admittance into UW-Madison. However, in 1999, I was accepted based on multiple factors.

## ACT: Scoring Mapped to Percentages Based on ACT Weighting Scheme

Here’s the full mapping according to the weighted scoring for each section in the ACT:

 ACT Score Points – Low % – Low Points – High % – High 36 214 99.5349 215 100.0000 35 206 95.8140 214 99.5349 34 201 93.4884 211 98.1395 33 193 89.7674 208 96.7442 32 184 85.5814 204 94.8837 31 174 80.9302 200 93.0233 30 163 75.8140 196 91.1628 29 156 72.5581 191 88.8372 28 145 67.4419 186 86.5116 27 137 63.7209 181 84.1860 26 132 61.3953 175 81.3953 25 122 56.7442 170 79.0698 24 115 53.4884 166 77.2093 23 103 47.9070 162 75.3488 22 94 43.7209 156 72.5581 21 86 40.0000 151 70.2326 20 82 38.1395 146 67.9070 19 78 36.2791 140 65.1163 18 72 33.4884 136 63.2558 17 65 30.2326 130 60.4651 16 59 27.4419 126 58.6047 15 55 25.5814 119 55.3488 14 51 23.7209 114 53.0233 13 47 21.8605 107 49.7674 12 42 19.5349 99 46.0465 11 36 16.7442 91 42.3256 10 29 13.4884 83 38.6047 9 25 11.6279 75 34.8837 8 21 9.7674 69 32.0930 7 17 7.9070 65 30.2326 6 13 6.0465 57 26.5116 5 9 4.1860 47 21.8605 4 6 2.7907 37 17.2093 3 3 1.3953 28 13.0233 2 1 0.4651 19 8.8372 1 0 0.0000 8 3.7209

Hence as an exam, we can say an “A”-student should map to an ACT score of 30-36; a “B”-student should map to an ACT score of 26-29; a “C”-student should map to an ACT score of 21-25; a “D”-student should map to an ACT score of 17-20; and an “F”-student should fall below a score of 16. That’s the traditional 60/70/80/90 scoring as considered by the ACT.

But as we have seen, that’s not necessarily true. So how does the ACT adjust to meet reality? The real answer…? It shouldn’t. Instead, a student should construct a road map of where they see themselves in their college years. If a student wants to go to Harvard, they need to understand their admission criteria and apply themselves in such a way to meet the application criteria.

At the same time, it has been anecdotally proven time and time again that it ultimately does not matter which schools you go to for college; but rather how you use the resources offered to you in achieving your goals.

Take for instance, the tiny little school of Carroll University. The school has yielded more doctoral level researchers in STEM fields in the Intelligence Community than UW-Milwaukee just 30 miles away; all this despite UW-Milwaukee having a stronger mathematics department (it places undergraduates in masters and doctoral courses) and having a more selective process for admissions. And to hammer the idea home, Carroll University graduates between 3 and 10 mathematics students per year. Typically there are between 40,000 to 60,000 STEM graduates per year and roughly three percent are in math, statistics, and computer science fields.

This means that there are approximately 1200 to 2000 math graduates per year. This means Carroll University ranges between 0.1% and 0.8% of a graduating math community. However, it makes up for 1 of the roughly 2,000 Presidential Early Career Award in Science and Engineering (PECASE) awards; the highest honor given to mathematicians (as well as other STEM fields) from the United States. Doing the basic math, 3% of STEM graduates are mathematicians across the 2,000 awardees means that Carroll University makes up for 1.67% of PECASE award winners in mathematics; a return of 208% when compared to other colleges and universities.

The moral of the story? A single test does not define the quality of the student. The quality of the school does not indicate the performance of the student. All these items do is provide resources for a student to succeed. In the end, the external factors mean more than the exam. External factors will dictate the quality of education obtained.

But do not let this article be interpreted that the ACT is worthless. It is far from that. Not taking the ACT will show an external factor to a university of interest. Taking the ACT will show your competence at that singular time your ability to take a test on subjects you may or may not have had the opportunity to take in a time that you’re most likely not trained for. If anything, it’s a test that indicates how well you operate under pressure.  Which is merely just another external factor.