The empirical rule is a statistical rule which declares that for a normal distribution, almost all data will fall within three standard deviations of the mean. The empirical rule is most often used in statistics to anticipate final outcomes. After a standard deviation is calculated and before exact data can be collected, this rule can be used as a rough estimate of the outcome of the data. This probability can be used meanwhile since gathering appropriate data may be time-consuming or even impossible to obtain. The empirical rule is also used as a rough way to test a distribution's "normality". If too many data points fall outside the three standard deviation boundaries, this could suggest that the distribution is not normal

1. Mastering Statistics
Empirical Rule of Standard Deviation

2. Empirical Rule of Standard Deviation
- Only applies to Bell Shape Data!
Empirical rule for Std deviation:
“About 68% of the data lie within 1ϭ of the mean”
“About 95% of the data lie within 2ϭ of the mean”
“About 99.7% of the data lie within 3ϭ of the mean”
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 10 20 30 40 50 60 70
Grades Distribution
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 10 20 30 40 50 60 70
Grades Distribution
-1ϭ
-2ϭ
1ϭ
2ϭ

3. Empirical Rule of Standard Deviation
Problem: Average weight of newborn babies is bell shaped with mean of
3325 grams and std. dev. of 571 grams. What percentage of babies
weight between 2183 and 4467 grams?
- Bell shape
- µ = 3325
- 1ϭ= 571
µ + 1ϭ = 3325+ 571= 3896; µ +2ϭ = 3325 + 2*571= 4467g
µ - 1ϭ = 3325 - 571= 3896; µ - 2ϭ = 3325 - 2*571= 2183g
- The empirical rule state that:
“About 95% of the data lie within 2ϭ of the mean”

4. Empirical Rule of Standard Deviation
Problem: Starting salary for graduates is bell shaped with mean of $25,400 and std.dev. Of $1,300.
what percentage of graduates have starting salary between $22,800 and 28,000
- Bell shape
- µ = $25,400
- Ϭ = $1,300
µ +Ϭ = $26,700; µ +2*Ϭ = $28000
µ -Ϭ = $24,100; µ -2*Ϭ = $22,800
About 95% have salary between $22,800 and 28,000
Problem: Electric bills for May are bell shaped with a mean of $119 and std dev of 22. what percent of
electric bills are less than $163
- µ = $119
- Ϭ = $163
- µ +Ϭ = $141; µ +2*Ϭ = $163;
- 95% are within 2*Ϭ; 5% outside and 2.5% from the “outside” are on the negative side of the bell
- Total = 95% + 2.5% = 97.5% less than $163