image - Statistics for Managers Using Microsoft Excel Self Study W 55H\u00a7\u00ae\u00a9MGQO\u00ae.9134 The Chebyshev Rule For heavily skewed sets of data and data sets

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Unformatted text preview: Statistics for Managers Using Microsoft Excel Self Study W 55H§®©MGQO® .9134 The Chebyshev Rule For heavily skewed sets of data and data sets that do not appear to be normally distrib— uted, you should use the Chebyshev rule instead of the empirical rule. The Chebyshev rule (see reference 2) states that for any data set, regardless of shape, the percentage of values that are found within distances of k standard deviations from the mean must be at least 1 (I — 7) X 100%: k You can use this rule for any value of k greater than 1, For example, consider k = 2. The Chebyshev rule states that at least [ 1 — (1/2) 2] X 100% = 75% of the values must be found within i2 standard deviations of the mean. The Chebyshev rule is very general and applies to any distribution. The rule indicates at least what percentage of the values fall within a given distance from the mean, However, if the data set is approximately bellmshaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean. Table 3,7 compares the Chebyshev and em— pirical rules. TABLE 3.7 H ow Data Vary Around % of Values Found In Intervals Around the Mean the Mean Chebyshev Empirical Rule Interval (any distribution) (normal distribution) See 59m?” E634 l” the _ ( p, — 0-, ,u, + 0-) At least 0% Approximately 68% Excel Gurcle for a description A 1 75‘? A . 1 95 (7 ofthe VE-Variability (M — 2m M + 20) t east 0 pprOXfInate y o workbook that allows you (,u, — 30', p, + 30') At least 88.89% Approxunately 99.7% to explore the empirical and Chebyshev rules. -I' ,- --—.I - 4-. A — it _ '___ T'J________'l_ *1 1A _ _______'l_;_'____ _I_‘r"1 1'.L---1__LJ_1__ _J'_‘__‘l_ '__ 1_________ J._ 1_____ _ _______ 11"." ____'__1_L ...
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