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204 3.4 measures of position

# 204 3.4 measures of position - 3.4 Measures of Position...

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3.4 Measures of Position Chebyshev's Theorm For any set of data (including populations and samples) and any constant k > 1, the proportion of the data that lies within k standard deviations of the mean is at least : 1 - As an example of this theorem let's consider the following set of data on the travel expenses of the 12 members of a university's physics department (in dollars) 0 0 173 378 441 733 759 857 958 985 1434 2063 The sample standard deviation of this data is 602.26. The sample mean is 731.75. According to Chebyshev’s theorem 0.55 = 1 - of the data is within 1.5 standard deviations of the mean. 11 of 12 values are between 731.75 - 1.5(602.26) and 731.75 + 1.5(602.26) -171.64 and 1635.14 Thus over 91.66 % of the data is within 1.5 standard deviations of the mean, which is considerably more than the conservative Chebyshev estimate of 55%. For the bell shaped distributions called Normal distributions, the percent of the data within k std. devs. is higher than is guaranteed by Chebyshev’s inequality. The following is called the

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204 3.4 measures of position - 3.4 Measures of Position...

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