STA6166 F06-6 Interpreting Shape, Center, and Spread

STA6166 F06-6 Interpreting Shape, Center, and Spread -...

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Topic (6) INTERPRETING SHAPE, CENTER AND SPREAD 6-1 Topic (6) INTERPRETING SHAPE, CENTER AND SPREAD In addition to simply describing the frequency distribution of a set of data we can also make use of the following. 1. The EMPIRICAL RULE : If the data set displays a frequency distribution that is somewhat symmetric, unimodal, without much skew, and approximately equal length tails then the following is true: a) about 68% of the observations are within 1 standard deviation of the mean, i.e. fall between s x and s x + s x ± = b) about 95% of the observations are within 2 standard deviations of the mean, i.e. fall between s x and s x 2 2 + s x 2 ± = c) > 99% of the observations are within 3 standard deviations of the mean, i.e. fall between s x and s x 3 3 + s x 3 ± =
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Topic (6) INTERPRETING SHAPE, CENTER AND SPREAD 6-2 The Empirical Rule is useful for summarizing datasets that display approximately Normal shapes. EXAMPLE
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STA6166 F06-6 Interpreting Shape, Center, and Spread -...

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