# What uses do Z-scores serve?

May 19th, 2015
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Z-scores, or standardized scores, can specifically describe the relative standing of every score in a distribution. • serves as a reference point: Are you above or below average?•  serves as a yardstick: How much are you above or below the average

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Z-ScoresZ-scores, or standardized scores, can specifically describe the relative standing of every score in a distribution.serves as a reference point: Are you above or below average? serves as a yardstick: How much are you above or below the average?What uses do Z-scores serve?1. Tell exact location of a score in a distributionJohnny is 10 years old and weighs 45 lbs.How does his wt. compare to other 10 yr old boys? 2. Compare scores across different distributionsJill scored 63 on her chemistry test & 47 on her biology testOn which test did she perform better?How are Z-scores calculated?If you know & of a distribution, you can calculate a Z-score for any value in that distribution.Formula: z = Deviation from in SD unitsRelative status, location, of a raw score (X)z-score has 2 parts:Sign tells you if score is above (+) or below (-) Value tells you the magnitude of distance in SD unitsConverting a raw score into a Z-score: Example:The average pregnancy lasts 266 days, w/ a standard deviation of 16 days Laura gave birth after 273 days?Lets convert this to a Z-score using the formula: z = X = 273 = 266 = 16z = = +0.4375Converting a Z-score to a raw score: Example:The length of Ellens pregnancy results in a Z-score of 1.25. How many days was she pregnant?Lets convert this to a Z-score using the formula: X = Z = -1.25 = 266 = 16X = 266 + (-1.25)(16)X = 246 days Z Distribu

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