The Normal Curve
Before we leave the standard deviation, it's a good time to learn a little more about the normal curve. We'll be coming back to it later.
First, why is it called the normal curve? The reason is that so many things in life are distributed in the shape of this curve: IQ, strength, height, weight, musical ability, resistance to disease, and so on. Not everything is normally distributed, but most things are. Thus the term normal curve.
In Figure 6, we have a set of scores which are normally distributed. The range is from 0 to 200, the mean and median are 100, and the standard deviation is 20. In a normal curve, the standard deviation indicates precisely how the scores are distributed. Note that the percentage of scores is marked off by standard deviations on either side of the mean. In the range between 80 and 120 (that’s one standard deviation on either side of the mean), there are 68.26% of the cases. In other words, in a normal distribution, roughly two thirds of the scores lie between one standard deviation on either side of the mean. If we go out to two standard deviations on either side of the mean, we will include 95.44% of the scores; and if we go out three standard deviations, that will encompass 98.74% of the scores; and so on.
Another way to think about this is to realize that in this distribution, if you have a score that’s within one standard deviation of the mean, i.e., between 80 and 120, that’s pretty average—two thirds of the people are concentrated in that range. But if you have a score that’s two or three standard deviations away from the mean, that is clearly a deviant score, i.e., very high or very low. Only a small percent of the cases lie that far out from the mean.
Below is a description of a normal curve with standard deviation distributions. Note the 1, -1, 2, -2, etc. This represents 1 standard deviation from the mean (or average). One standard deviation from the average (mean) also indicates that 68% of the the data average falls within this range. Two standard deviations indicates that 95% of the data falls within this range.