Normal Distribution

Because much of what we will discuss in subsequent sections is based on the normal distribution, it's probably worthwhile to spend a little more time exploring this magical distribution.

It has been observed that the natural variation of many variables tends to follow a bell-shaped distribution, with most values clustered symmetrically near the mean and with a few values falling in the tails. The shape of this bell curve can be expressed mathematically in terms of the two statistical concepts we have discussed—the mean and the SD. In other words, if you know the mean and SD of your data, and if you are justified in assuming that the data follow a normal distribution, then you can tell precisely the shape of the curve by plugging the mean and SD into the formula for the normal curve.

If you look at the calculated curve superimposed on your mean and SD, you would see something like Figure 2-5.

Of the values, 68% fall within one SD of the mean, 95.5% fall within two SDs, and 2.3% fall in each tail. This is true for every normal distribution, not just this curve, and comes from the theoretical shape of the curve. This is a good thing because our original figures, such as those in Figure 2-2, don't really give much of an idea of what is happening on the tails. But we can use all the data to get a good estimate of the mean and SD, and then draw a nice smooth curve through it.

Figure 2-5 The normal distribution (bell-shaped curve).

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