EmpiricalRule_f10

# EmpiricalRule_f10 - Statistics 3011 Course Notes Supplement...

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Statistics 3011, Course Notes Supplement 1 September 22, 2010 Empirical Rule On p. 28 of the course notes, a “General Rule” is given that usually nearly all of the ob- servations will fall within 3 s of x (i.e., within 3 standard deviations of the mean). This “General Rule” is one part of the Empirical Rule , which is given below and discussed in the textbook on p. 61. The Empirical Rule states that if a distribution of data is bell-shaped, then approximately 68% of the observations fall within 1 standard deviation of the mean, that is, between x - s and x + s (denoted x ± s ). 95% of the observations fall within 2 standard deviations of the mean ( x ± 2 s ) All or nearly all observations fall within 3 standard deviations of the mean ( x ± 3 s ) If the distribution of the data is symmetric, the approximations given by the Empirical Rule tend to be fairly close. However, if the distribution is highly skewed or highly discrete, or if the sample is small, then the approximation may be poor. The Empirical Rule in Practice

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EmpiricalRule_f10 - Statistics 3011 Course Notes Supplement...

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