Mercy! Mercy! That Dang Nabed PERCY!

The "So What" Question

I saw a book title at Barnes and Noble, which was titled something like, “Why A students work for C students.” I should have bought it and think I’ll have Linda order it for me.

When I was in school the range of acceptable grades went from D to A. The grade D was set somewhere in the 60% bracket. The grade C was somewhere in the 70% bracket, the B grade in the 80% bracket and A in the 90% bracket. I suppose this is the case in education systems throughout the world but I am hardly an expert on systems used in other countries.

The question that comes to mind is “Where did these arbritary cutoffs come from?" Again I'm not sure but it seems to me that in a mass education system there had to be some sort of value assigned to students that would indicate their mastery of the subject matter. So, a grade below 60% mastery of the material became an unacceptable outcome. (FAILURE) A grade in the 70% range was barely acceptable. A grade in the 80% bracket was OK and a grade above the 90% threshold was considered good. Thus below a D grade showed unmastery and a grade of A showed a strong mastery.

I assume that there was a statistical model that formed the underpinning of this construct and that Standard Deviation (SD) was at the root of it. So, HOW DOES SD WORK? you might ask and I encourage you to Google the term in order to refresh your memory or learn from scratch what that statistic measures.

I was first introduced to SD in a statistics course in graduate school. I must shamefully admit that at the time I never fully grasped what it meant. Sure, I memorized the formulas and learned to plug in the values and got a B in the course but the truth is that the real meaning didn’t sink in for about a year, until one morning I woke up and realized I suddenly understood what the math was trying to tell me. What follows is a brief explanation of SD through the lens of Percy Goodfellow.

We often hear the term “Average” batted around when somebody tries to make a point. They might say something like, “The Average frog lives twenty years.” Hmmm, you might think, Twenty years seems a long time for a frog to live but who am I to question? Obviously some academic took the time to calculate an average life span taken from all the species of frogs and hence he/she must know what they are talking about. Unless of course it’s something they made up to fill out their master’s thesis.

Assuming the person making the statement is not telling an outright lie, an astute listener should have a red flag go up whenever they hear the word “Average.” This is because some averages are good indicators of central tendency and some absolutely SUCK! For example suppose there were three students in a special needs class. One had an IQ of 35, another one of 95 and the third one of 450. If you add those up and divide by three the “average” doesn’t tell you a damn thing. On the other hand if there are 10 special needs students with IQs of 95, 96, 98, 94, 92, 101, 97, 95, 93 and 100, this set of data is going to give you a pretty good average. A teacher could take this average and have a pretty good idea of what the IQ of the next student coming through the door would be. Get it? I’m sure you do. Some averages are good predictors and some aren’t worth a “Doo-Doo.”

So what the SD statistic is saying is how good an Average is. The calculation is not that complicated and the result shows a number useful in determining a confidence interval. Supposed the SD for a data set is 3, where the average is 96. If you plus and minus the 3 you have a range of from 93 to 99. If you were a gambler you could be 68% confident that the next number in the data set would be between 93 and 99. However, it gets even better. If you double that 3 to a 6 you get a range of from 90 to 102. Here you can be 95% confident that the next number will be somewhere between the two. Finally, if you add three more and make it 9, this is called 3 SDs and here you can be 99% confident that the next number will be between 87 and 105. I hope you get the idea.

Now, I know I’m boring many of my readers and many more don’t have a clue of what I’m talking about. The reason I'm doing this is because tomorrow I plan to tackle the “So What” question.