How to Understand the Bell Curve, Standard Deviation, and Normal Distributions

The bell curve is the graphical form of a normal distribution. It looks like a bell as seen from the side, hence its name. Sometimes it is called a Gaussian distribution because the mathematician Friedrich Gauss invented it. Most natural quantities follow a normal distribution, hence the name. Human height for a random sample follows a normal distribution, for example. So does IQ.

The standard deviation for IQ is 15 points. 68% of people are within plus or minus 15 points of the average IQ, which is 100. 95% of people are within plus or minus two standard deviations or 30 points of the average IQ. 99.7% of people are within plus or minus three standard deviations or 45 points of the average IQ.

In manufacturing, the phrase Six Sigma refers to a defect rate less than 0.3%. In other words, 99.7% of the product is good. So if a car manufacturer makes 1,000 cars per day and only 3 fail the quality inspection, that process meets the Six Sigma standard. Sigma is the name of the Greek letter often used to represent standard deviation, so Six Sigma means plus or minus three standard deviations. 

While there are other distributions, if they data does not fit the profile of a bell curve, it might mean that there was a flaw in the data collection. Perhaps the sample size was too small or not random enough.