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Chapter 3: Measures of Variability
within three standard deviations of the mean. The three sigma rule is
illustrated in
Figure 3-26
.
Figure 3-26:
Illustration of the three sigma rule
Numerical Illustration for the Three Sigma Rule
Recall the chest size data given previously. The distribution for this data set
is displayed in
Figure 3-27
along with
red vertical lines
at
=
39.832 – 3
2.05 = 33.682 and
= 39.832 + 3
2.05 = 45.982.
Observe that the chest size values to be included in the computations ranges
over almost the entire set of chest size values. The range of values goes from
34 to 46. The sum of the corresponding relative frequencies (probabilities)
is approximately 0.9986. Refer to
Figure 3-28
for the computed
probabilities. That is, approximately 99.86% (close to 99.7%) of the values
will lie within three standard deviations of the mean.