Empirical Rule

The Empirical Rule is also referred to as the 68-95-99.7% Rule. What it tells us is that for a normally distributed variable, the following are true:
  • Approximately 68% of the data lie within 1 standard deviation of the mean.
  • Approximately 95% of the data lie within 2 standard deviations of the mean.
  • Approximately 99.7% of the data lie within 3 standard deviations of the mean.
This translates into the following picture:


Most students find it easier to deal with the areas in each section of the curve, rather than the middle probabilities above:



Next: See how we can apply the Empirical Rule to calculate approximate percentages for any normal distribution.

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