The 68% Rule

Recall what standard deviation is:  it is the average distance of scores from the mean of a distribution.  We can examine the difference score for any particular individual and see how many standard deviations they are from the mean to get an idea of how extreme that score is.  One extremely important characteristic of the normal distribution is what we will call the 68% Rule.  The 68% Rule states that about 68% of cases lie within one standard deviation unit of the mean in a normal distribution.

```68% Rule

About 68% of cases lie within one standard deviation unit of the mean in a normal distribution.```

Note that when we say “one standard deviation unit” we are talking about both sides of the curve.  In other words, we are saying that 68% of people will fall within the interval defined by negative one standard deviation from the mean and positive one standard deviation from the mean.  Let us say, for example, that a test has a mean of 100 and a standard deviation of 10.  In such a case, 68% of those taking the test would score between 90 and 110.  Remember that this rule only applies to a normal distribution!  The less normal the curve, the less accurate the rule.

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`Last Modified:  06/03/2021`

2 thoughts on “The 68% Rule”

1. Paul Scheuer says:

I cannot see why the 68% rule comes from?
Why did de Moivre’s took choice
Why not a 70% rule

1. The mathematics of the normal curve defines the area under the curve. It’s actually a long decimal number, which rounds to 68%. It wasn’t arbitrary.

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