The 689599.7 Rule
For Normal Distributions
This rule applies generally to a variable X
having normal (bellshaped or moundshaped) distribution
with mean "mu" (the greek letter) and standard
deviation "sigma" (the greek letter). However,
this rule does not apply to distributions that are not
normal.
Note: Generally, to say "within A of B"
means "between BA and B+A." For instance,
"within 2 of 5" means "between 5  2 = 3
and 5 + 2 = 7," in short "between 3 and
7."
Approximately 68% of the observations fall within 1
standard deviation of the mean
Note that the range "within one standard
deviation of the mean" is highlighted in green. The area
under the curve over this range is the relative frequency
of observations in the range. That is, 0.68 = 68% of the
observations fall within one standard deviation of the
mean, or, 68% of the observations are between (mu 
sigma) and (mu + sigma).
Below the axis, in red,
is another set of numbers. These numbers are simply
measures of standard deviations from the mean. In working
with the variable X we will often find it
necessary to convert into units of standard deviations
from the mean. When the variable is measured this way,
the letter Z is commonly used.
Approximately 95% of the observations fall within 2
standard deviations of the mean
Approximately 99.7% of the observations fall within 3
standard deviations of the mean
Only a small fraction of observations (0.3% = 1 in
333) lie outside this range.
Another way of looking at it!
This is merely a consequence of the 689599.7 rule.
Want to see an example? Check out the distribution of weights of adult males.
