2-3(cont)_mean_sd_together

2-3(cont)_mean_sd_together - 2.3 (cont.) Using the Mean and...

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1 2.3 (cont.) Using the Mean and Standard Deviation Together 68-95-99.7 rule z-scores
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2 Business interpretation of standard deviation The “risk” of an investment is usually the standard deviation of some measure of return on the investment stock risk: standard deviation of stock price bond fund risk: standard deviation of annual rate of return
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3 68-95-99.7 rule Mean and Standard Deviation (numerical) Histogram (graphical) 68-95-99.7 rule
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4 The 68-95-99.7 rule; applies only to mound-shaped data - + - + - + approximately 68% of the measurements are within 1 standard deviation of the mean, that is, in approx. 95% of the measurements are within 2 stand. dev. of the mean, i.e., in almost all the measurements are within 3 stan. dev of the mean, i.e., in ( , ) ( , ) ( , ) x s x s x s x s x s x s 2 2 3 3
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68-95-99.7 rule: 68% within 1 stan. dev. of the mean 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 68% 34% 34% x-s x x+s
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6 68-95-99.7 rule: 95% within 2 stan. dev. of the mean 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 95% 47.5% 47.5% x-2s x x+2s
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7 Example: class pulse rates 53 64 67 67 70 76 77 77 78 83 84 85 85 89 90 90 90 90 91 96 98 103 140 037 . 17 48 . 84 = = s x
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2-3(cont)_mean_sd_together - 2.3 (cont.) Using the Mean and...

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