# lec06 - STATISTICS 13 Lecture 6 Oct 6 2010 Review Measures...

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STATISTICS 13 Lecture 6 Oct 6, 2010

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Review Measures of variability – Range – Variance – Standard deviation: properties – Empirical rule for bell-shaped distribution Tchebysheff’s Theorem
Measures of Relative Standing What is the position of one measurement relative to the other measurements ? In measurement scale : how many standard deviation away from the mean does the measurement lie ? z-score: s x x z = score - s s 5 = x 9 = x s = 2 s

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Significance of z-scores Empirical rule : for bell-shaped data – About 95% of the measurements are within 2 std. dev. of mean Implication: for bell-shaped data – z-score between -2 and 2: typical measurements – z-score above 3 in absolute value: ``extreme” measurements, could be outliers
Significance of z-score (cont.) z-score in various regions: for bell shaped distributions May be Outlier May be Outlier Typical z -3 -2 -1 0 1 2 3 Unusual

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Example: Age of CEO mean=51.47, s=8.92 32 33 36 37 38 40 41 43 43 44 44 45 45 45 45 (-2.2 -2.1 -1.7 -1.6 -1.5 -1.3 -1.2 -0.9 -0.9 -0.8 -0.8 -0.7 -0.7 -0.7 -0.7) 46 46 47 47 47 48
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lec06 - STATISTICS 13 Lecture 6 Oct 6 2010 Review Measures...

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