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Section 3 Week in Review 2011

# Section 3 Week in Review 2011 - 75 89 94 AEM 2100 Spring...

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μ ≥ 75% ≥ 89% ≥ 94% - 2σ + 2σ - 3σ + 3σ - 4σ + 4σ 95% 100% AEM 2100, Spring 2011 WEEK IN REVIEW Feb 14-17 SECTION 3 Uses of the Mean and Standard Deviation: Z-Score : indicates the number of standard deviations a data value is from the mean ( unitless ). (population) (sample) A positive z-score indicates a value above the mean A negative z-score indicates a value below the mean Chebyshev’s Theorem : For any value k, the proportion of data values found within k standard deviations from the mean will be at least 1-(1/k 2 ). Note: k>1. Applies to any data set regardless of the shape of its distribution. (See diagram below) Empirical Rule : Applies only to mound-shaped data , and states that: Approx. 68% of data values will fall within 1 standard deviation above and below the mean Approx. 95% of data values will fall within 2 standard deviations above and below the mean Approx. 100% of data values will fall within 3 standard deviations above and below the mean (See diagram below)

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Section 3 Week in Review 2011 - 75 89 94 AEM 2100 Spring...

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