Empirical Rule (68-95-99.7%) Empirical Rule For data with a (symmetric) bell-shaped distribution, the standard deviation has the following characteristics. About 68% of the data lie within one standard deviation of the mean. About 95% of the data lie within two standard deviations of the mean. About 99.7% of the data lie within three standard deviation of the mean.

Empirical Rule (68-95-99.7%) 34% 34% 2.35% 2.35% 13.5% 13.5% –4 –3 –2 99.7% within 3 standard deviations 95% within 2 standard deviations 68% within 1 standard deviation –4 –3 –2 –1 1 2 3 4 34% 34% 2.35% 2.35% 13.5% 13.5%

Using the Empirical Rule Example: The mean value of homes on a street is $125 thousand with a standard deviation of $5 thousand. The data set has a bell shaped distribution. Estimate the percent of homes between $120 and $130 thousand. 125 130 135 120 140 145 115 110 105 68% μ – σ μ μ + σ 68% of the houses have a value between $120 and $130 thousand.