Statistics 3011, Course Notes Supplement 1
September 22, 2010
Empirical Rule
On p. 28 of the course notes, a “General Rule” is given that usually nearly all of the ob
servations will fall within 3
s
of
x
(i.e., within 3 standard deviations of the mean).
This “General Rule” is one part of the
Empirical Rule
, which is given below and discussed
in the textbook on p. 61.
The Empirical Rule states that if a distribution of data is bellshaped, then approximately
•
68% of the observations fall within 1 standard deviation of the mean, that is, between
x

s
and
x
+
s
(denoted
x
±
s
).
•
95% of the observations fall within 2 standard deviations of the mean (
x
±
2
s
)
•
All or nearly all observations fall within 3 standard deviations of the mean (
x
±
3
s
)
If the distribution of the data is symmetric, the approximations given by the Empirical Rule
tend to be fairly close. However, if the distribution is highly skewed or highly discrete, or
if the sample is small, then the approximation may be poor.
The Empirical Rule in Practice
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 Spring '11
 Statistics, Empirical Rule, Standard Deviation, 68%, 250 days, 13 days, 237 days

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