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that if you go out 2 standard deviations on both sides of the mean in a normal distribution, you will find approximately 95% of the cases.
Example 1
The mean for a group equals 35 and the standard deviation equals 6. Two standard deviations equals 12 points (2 x 6 = 12). Thus, if you (a) go up 12 points from the mean (35 + 12 = 47) and (b) go down 12 points from the mean (35 - 12 = 23), you have identified the scores (47 and 23) between which approximately 95% of the cases lie.
The 99% rule says that if we go up and down 3 standard deviations from the mean, we find approximately 99% of the cases.
For the information in Example 1, multiply 3 times the standard deviation (3 x 6 = 18). Going up and down 18 points from the mean yields these scores: 53 and 17.
Example 2
If the mean = 35 and the standard deviation 6, then approximately:
68% of the cases lie between 29 and 41;
95% of the cases lie between 23 and 47; and
99% of
the cases lie between 17 and 53.
You can see that almost all cases (99%) in a normal distribution lie within 3 standard deviations of the mean. Thus, for practical purposes we can say that a normal distribution has only six standard deviations - three above the mean and three below the mean.
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