Chapter6 stat

# Chapter6 stat - Chapter 6 The Standard Deviation as a Ruler...

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Chapter 6 The Standard Deviation as a Ruler and the Normal Model

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Standardize To understand how an individual value is from all the values, we standardized the value, finding how many standard deviations the value is away from the mean. To find this out, we take the deviation and then divide it by the standard deviation.
Z-score We call the resulting values standardized values, and denote it with the letter z. Usually we call them z-scores. s y y z _ - =

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Quick Example The average age of all the players on a football team is 32 with a standard deviation of 3. If a player on the team is 25, how many standard deviations is 25 away from the mean? 33 . 2 3 32 25 - = - = z
Same Equation, Different Notation Another way of finding the z-score is σ μ - = y z

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How does Standardizing Change the Distribution? Standardizing into z-scores does not change the shape of the distribution of a variable. Standardizing into z-scores changes the center by making the mean 0. Standardizing into z-scores changes the spread by making the s.d. 1.
Normal Models There is no universal standard for z-scores, but there is a model that shows up over and over in Statistics. You may have heard of “bell-shaped curves.” Statisticians call them Normal models.

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## This note was uploaded on 04/07/2008 for the course MAT 108 taught by Professor Lamatina during the Spring '08 term at SUNY Albany.

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Chapter6 stat - Chapter 6 The Standard Deviation as a Ruler...

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