cheby - seventy five percent will fall within two standard...

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Kyle Daniele 10/1/08 Russian mathematician Pafnuty Chebyshev discovered that the fraction of observations falling between two distinct values, whose differences from the mean have the same absolute value, is related to the variance of the population. This allowed him to prove a theorem in which can be used for any distribution of data. For any set of data, population or sample, and for any constant “k” greater than one, the proportion of the data that must lie within “k” standard deviations on either side of the mean is at least 1-1/ k squared. What does this mean? Data can be spread about the mean by skewed, symmetric, or any other shape for that matter by using the Chebyshev theorem This theorem provides a few useful rules in statistics. First, no information can be obtained on the fraction of values falling within one standard deviation. Second, at least
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Unformatted text preview: seventy five percent will fall within two standard deviations. Third, at least 88.9 percent will fall within three standard deviations. Finally, at least 93.8 percent will fall within four standard deviations. These are the minimum percentages of data that must fall within within the specified number of standard deviations of the mean. However, if the distribution is mound-shaped, an even greater percentage of data will fall into the specified intervals, which involves the Empirical Rule. This theorem is good for almost everything, from butterflies to the orbits of the planets, because it can be applied to everything. As mentioned earlier, any set of data can be represented using Chebyshev’s theorem....
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This note was uploaded on 12/14/2009 for the course ENG 101 taught by Professor Chang during the Spring '09 term at 東京国際大学.

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