1. Chebyshev's Rule:
Chebyshev's rule applies to any sample of measurements regardless of the shape of their
distribution. The rule states that:
It is possible that none of the measurements will fall within one standard deviation of the mean.
At least 75% (or 3/4) of the measurements will fall within two standard deviations of the mean,
and 89% (or 8/9) of the measurements will fall within three standard deviations of the mean.
Generally, according to this rule, at least 1 - (1/k squared) of the measurements will fall within
[(mean + - (k) standard deviation)], i.e., within k standard deviation of the mean, where k is any
number greater than one. For example, if k = 2.8, at least .87 of all values fall within (mean + -
2.8 x standard deviation), because 1 - (1/k squared) = 1 - (1/7.84) = 1 - 0.13 = 0.87.
Empirical Rule:
This rule generally applies to mound-shaped data, but specifically to the data that are normally
distributed, i.e., bell shaped. The rule is as follows:
Approximately 68% of the measurements (data) will fall within one standard deviation of the
mean, 95% fall within two standard deviations, and 97.7% (or almost 100% ) fall within three
standard deviations.
For example, in the height problem, the mean height was 70 inches with a standard deviation of
3.4 inches. Thus, 68% of the heights fall between 66.6 and 73.4 inches, one standard deviation,
i.e., (mean + 1 standard deviation) = (70 + 3.4) = 73.4, and (mean - 1 standard deviation) = 66.6.
Ninety five percent (95%) of the heights fall betweeen 63.2 and 76.8 inchesd, two standard
deviations. Ninety nine and seven tenths percent (99.7%) fall between 59.8 and 80.2 inches,
three standard deviations.
Also see the link,
http://business.clayton.edu/arjomand/bus…
I have taken the detail from the above link.