The Normal Curve and Empirical Rule

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The distributions of most continuous random variables will follow the shape of the normal curve.

Figure 1.

On the normal curve, mean, median, and mode all exist at the center.

Figure 2.

The graph changes direction at inflection points. These first points mark the distance of one standard deviation from the mean.

Figure 3.

The Empirical Rule
The empirical rule states that: 68% of all values fall within 1 standard deviation of the mean. 95% of all values fall within 2 standard deviations of the mean. 99.7% of all values fall within 3 standard deviations of the mean.

The Empirical Rule

The empirical rule states that:

68% of all values fall within 1 standard deviation of the mean.

95% of all values fall within 2 standard deviations of the mean.

99.7% of all values fall within 3 standard deviations of the mean.