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Chapter 3: Measures of Variability
Figure 3-22:
Computed probabilities
to be included
for the One-sigma rule for the Chest
Size data
Two Sigma Rule
Approximately 95 percent of the data values will lie within two standard
deviations of the mean for
any
bell-shaped distribution. That is, regardless
of the values for the mean and standard deviation of the distribution, the
probability that the variable will be within two standard deviation of the
mean is approximately equal to 0.95. This means that approximately 5% of
the values will lie outside of two standard deviations of the mean. Thus, if
we sample from a bell-shaped population we should expect about one in
every twenty (approximately 5%) of the values will lie outside two standard
deviations from the mean. Equivalently, we should expect about nineteen
out of every twenty (approximately 95%) values will lie within two standard
deviations of the mean. The two sigma rule is illustrated in
Figure 3-23
.