Empirical Rule and Chebyshev’s Theorem
Chebyshev's theorem and the empirical rule both attempt to make generalizations about
distributions of data. However, the empirical rule only applies to bellshaped
distributions. Chebyshev's can be applied to any distribution (regardless of shape). This
makes Chebyshev's more versatile. But with the flexibility gained, there is a price tag.
Chebyshev's is more conservative in its estimates because it accommodates all
distributions.
The Empirical Rule:
The empirical rule is specific to bellshaped distributions. You can see a picture of one on
page 96 of your text. You will see more of the bellshaped curve (also called the normal
distribution) in chapter 6 and several other courses. But for now in this chapter you
should learn the general rule that if data is bellshaped, then the 68/95/99.7 percent rule
applies. Because it assumes bellshaped curve, it is more specific in determining the
percent of data values that are around the mean.
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 Spring '08
 Nabavi
 Empirical Rule, Normal Distribution, Standard Deviation, data values

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