Sometimes we’re told numbers that just don’t seem right. Even when the math is shown to us, the answer doesn’t align with the world we see around us. Rather than burying our heads in the sand and denying the math, or just conceding that our feelings are wrong and accepting the ‘fact’ as presented, at We All Count, we recommend a third approach in which we ask: “Is there anything that seems objective that might actually be a subjective perspective?”. We find that when answering human questions with math thinking of the results as ‘an’ answer and not ‘the’ answer leads to better outcomes with more effective and equitable data science.
Imagine that you are a student who feels that the average class size in your school is pretty large, yet you’re told that the average class size is normal and smaller than you thought. What if the simple average you were given was only one perspective on the issue and not THE perspective? At We All Count, we know that even the simplest math can be sneakily subjective.
Math is a tool. It doesn’t have any more of a perspective than a hammer or more opinions than a cheese grater. Humans, on the other hand, are full of bias. They have unique perspectives, assumptions, and worldviews embedded so deeply, that it can feel like they are simply expressions of our objective reality. When humans use data science, we need to carefully identify what perspective we’re bringing to the task, and never believe that we aren’t bringing preconceived ideas with us, even in the simplest cases.
Let’s try an experiment. We’re going to work on a simple average or mean. There are three classrooms, one with 5 students, one with ten students, and another with 15 students. What is the average class size across the three classrooms? You might have said 10? If you said ten, you’re correct. Your response also reflects a specific social power structure in which you imagined the average from the perspective of the teachers. What if I said that 12 is also a correct average class size, from the perspective of the students?
In the first example, we imagined the three classrooms from a single perspective each, 5 students, plus 10 students, plus 15 students, which amount to 30 divided by 3 perspectives. This gives us the average class size from the teacher’s point of view.
Now imagine it from the students’ point of view.
The math looks like this: 5+5+5+5+5+10+10+10+10+10+10+10+10+10 = 350 / 30 = 11.67
There are 5 students experiencing a classroom of 5, 10 students experiencing a classroom of 10, and 15 students experiencing a classroom of 15. Instead of dividing by 3 teachers, we’re going to divide by 30 students because we’re incorporating all of their perspectives. This average reflects the average class size from the perspective of the students.
If you feel angry or confused right now, you’re not alone. Even us, the people making this video have a hard time wrapping our heads around this. That strong emotional reaction is often a good indicator that you’re challenging an entrenched concept that you believe on a level beyond just math. Take a breath and look at the numbers again. Open yourself intellectually to the idea that this math also makes sense.
It is important to understand that BOTH OF THESE ANSWERS ARE CORRECT. Both 10 and 12 are meaningful but different averages for measuring this situation. Both have their uses depending on what question you’re asking. This isn’t some neat trick, it’s a reminder to always approach data science with an awareness of your preconceived notions and assumed perspectives. Good data science relies on the ability to identify and account for the human side of math, otherwise, our algorithms and equations will masquerade as ‘objective’ when they are in fact expressions of the humans who made them.