Normal Distributions are Distributed Normally

Normal Distributions are Distributed Normally

If you have enough people or samples in any set of data, when measuring a variable it will always take on the characteristics of a Normal Distribution. What does that mean? Think Bell Curve.

I know everyone hates that thing, but it really does serve a purpose. Let's talk about test scores:

In a class of 60 students there is an average for the test score (out of a max of 100%) of say 75%. And there is a Standard Deviation of 8%. So if you look at a bell curve, 68% of the class would score between 83% (75% + 8%) and 67% (75% - 8%). This range of 67% to 83% is the distance from one standard deviation less than the average to one standard deviation greater than the average.

Most of the class average 68% will lie in the above range.

Two standard deviations away from the mean is...

59% to 92%: which means that 95% of the class scores between these two scores. Which makes a lot of sense if the teacher gave a fair test.

However it is unlikely very many people will score above 99% or bellow 51% on the test (3 standard deviations). In fact only about 2% of the class will get a score out side of the three standard deviation range.

So, what does this mean? Look at your GMAT scores for business school. Each time a test is administered, there is a sample of scores. So, on the day I took my GMAT I got a 610. There I no way to know what that means relative to everyone that has ever taken the GMAT, because there are differences and abnormalities from test year / month to the next test year / month.

How do schools help decipher your score? They use the percentiles. Every single time the percentile is understood to mean the same thing. How many people scored less than you did on the test? Based on YOUR sample. I scored 610. What does that mean? I was in the 92 percentile. So 92% of the people taking the test, around the same time as I did, scored less than I did.

This number 92% actually mean something. Some people say... I got a 610 too, but that is irrelevant. If they scored in the 70% percentile they technically did worse, because more people did better than they did.