The Bell Shape Curve

So what is this famous Bell Shape Curve ? Well it is has the "mean" or average in the middle and then it spreads out according to the standard deviation.

Lets say we have three class. Class A has scores of 100,90,80,70,60. Class B has scores of 100,100,80,60,60. And Class C has scores of 80,80,80,80,80.

Now if you were to find the "mean" or average of these classes they all have an 80 average. And if you were to find the "medium" or middle score, that would be 80 too. So some administrator who is not looking at the raw scores might concluded that these three classes are all the same.

But these three classes are not the same. Class B has two 100's and therefore two students who are not being challenged. Class B also has two 60's and therefore two students who are not catching onto the concepts being taught.

For Class C it looks like they took a "class test" or the teacher was sleeping during the testing.

Which brings us to the idea of why do we have grades to begin with. Most people think grades are to show how much the students have learned. But grades are not for that, they are distinguish one student from another.

That is why in education we like Class A distribution of grades 100,90,80,70,60.

So since the mean and medium are the same for these three classes we need another type of measurement. We want to know how the grades vary from each other. Or how they deviate. So we figure out a measurement called "standard deviation" or SD.

Most calculators or laptops have programs that can figure out the SD for a set of numbers. We no longer memorize these complicated formulas like we used to.

Lets look at our SAT scores. The national average is 1000 with a SD of 200.

The beauty of the Bell Shape Curve is that it can be used to show that 95% of the population of high school kids who take the SAT's are within 2 SD of the mean.

That means that 95% of the population scores somewhere from 600 to 1400 on the SAT's.

And that the only thing the SAT's can measure is that if you score somewhere between 600 and 1400 on the SAT, you are consider a "normal" student going to college.

By the way, research has shown that SAT scores is NOT a good predictor of how a student will do in college.

Another example is the IQ test. It takes your mental age and divides it by your biological age. So a 10 year old measuring with a 10 year old mentality would be 10/10 = 100.

Again we would have a standard deviation (SD) of 20, therefore 95% of the people are 2 SD away from the mean. In this case that would be 95% of the people would score somewhere between 60 and 140 on the IQ test.

And the only thing the IQ test can measure is that if you score somewhere between 60 and 140 you are considered to be have "normal" mentality.

Research has also shown that IQ test is NOT a good predictor on how a student will do in high school.