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# Chapter 6 - Chapter 6 Standardizing and Normal Model...

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Chapter 6 – Standardizing and Normal Model ActivStats: 6-1 to 6-4 Read: Chapter 6 Question: Who did better Bacher winning 800-m in 129 sec., or Prokhorova winning long jump with 660 cm jump? The average time for 800-m run was 137 sec. and the standard deviation was 8 sec, so Bacher’s time was (129 -137)/8 = -1.0 standard deviations below the average. The average jump was 600 cm., and the standard deviation was 30 cm., so Prokhorova’s jump was (660-600)/30 = 2 standard deviations above the average. Prokhorova did better . Standardizing DATA: 1 y 2 y ... n y y = mean s = standard deviation For each data point y the number s y y z - =

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is called the standardized value of y or z-score Mean of the standardized values is 0 Standard deviation of the standardized values is 1 Standardization does not change the shape of the distribution . Rescaling Data Adding a constant c to every data value adds the same constant to measures of center (mean, median, quartiles) but leaves measures of spread
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Chapter 6 - Chapter 6 Standardizing and Normal Model...

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