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Unformatted text preview: Lab 3 zScores, the Normal Curve, and Computer Graphs of Distributions Learning Objectives Define a zscore. Calculate zscores. State the mean and SD of the Standard Normal Curve. Use tabled values of the normal curve to estimate percentages of a distribution. Graph Distributions. What is a zscore? Zscore defined. A zscore tells the location of an observation in terms of standard deviations from the mean. If a zscore is zero, its on the mean. If a zscore is positive, its above the mean. If a zscore is negative, its below the mean. The value of the zscore tells how many standard deviations above or below the mean it is. A z score of 2 is 2 SDs above; 1 is 1 SD below. Zscore formulas To find a zscore, subtract the mean from the score and divide by the SD. A zscore for a population: A zscore for a sample:  = X z s X X z = Computing zscores from raw scores 5 3 2 2 1 5 3 2 4 .5 8 3 5 4 1.25 8 102 4.5 X X X s X s X X z = Computing zscores What is z? =10, =8, s=4, z = ? A: .5 =8, =10, s=2, z=? A: 1 =20, =15, s=5, z =? A: 1 X X X X X X Computing raw scores from zscores  Formulas To find a raw score, multiply the zscore by the SD and then add the mean. Population formula: Sample formula: + = z X X zs X + = Computing raw scores from zscores  Examples z s zs X=zs+ 1 3 2 3 52 3 264 2 8 81.5 4 165 X X Computing raw scores What is X?...
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 Fall '08
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