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Z-scores

Z-scores. Standard Scores . Different normal distributions vary based on the mean µ and the standard deviation ơ . The mean may be located anywhere on the x-axis. The bell-shape may be wide or narrow, depending on the value of the standard deviation ơ .

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Z-scores

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  1. Z-scores

  2. Standard Scores • Different normal distributions vary based on the mean µ and the standard deviation ơ. • The mean may be located anywhere on the x-axis. • The bell-shape may be wide or narrow, depending on the value of the standard deviation ơ. • Standard scores, also called z-scores, give the number of standard deviations that the original measurement is from the mean µ.

  3. Standard Scores • The z-score formula is • z-score • =given data value • = mean of the x-score distribution • = standard deviation of the x-score distribution

  4. Z Scores • The heights of 16-year-old males are normally distributed with mean 68 inches and a standard deviation 2 inches. Determine the z-score for: • 70 inches • 66 inches • pg 869 # 5 and 6

  5. Z Scores • Data below the mean will always have negative z-scores. • Data above the mean will always have positive z-scores. • The mean will always have a z-score of zero. • pg 869-870 # 7

  6. What is “Normal”? • If a z score is more than -2 but less than 2 then the data is considered normal. • If a z score is less than -2 or more than 2 it is considered unusual. • If a z score is less than -3 or more than 3 it is considered very unusual.

  7. Z Score Practice • pgs 871-873 #1-6

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