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

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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.
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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 A market sells an average of 25 newspapers a day with a standard deviation of 4. If the market sells 30 newspapers, how many standard deviations is 30 away from the mean? 25 . 1 4 25 30 = - = z
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Interpret A z-score of 1.25 says that the value of 30 is 1.25 standard deviations above the mean. A z-score of –1.25 (20 newspapers) says that the value of 20 is 1.25 standard deviations below the mean.
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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.
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Normal Models There is no universal standard for z-scores, but there is a model that shows up over and over in
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Chapter6 - Chapter 6 The Standard Deviation as a Ruler and...

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