1. Empirical Rule ( %)
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.

2. 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%

3. 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.