M119L06-page13 - results from Chebyshevs Theorem. The...

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(Lesson 6: Measures of Spread or Variation; 3-3) 3.27 Example 3 revisited The scores on a test have mean μ = 50 points and SD σ = 10 points . By Chebyshev’s Theorem (distribution free) By the Empirical Rule (assumes normality) What proportion of the values are within 1 SD of the mean (i.e., between 40 and 60 points)? (no information) About 68% What proportion of the values are within 2 SDs of the mean (i.e., between 30 and 70 points)? At least 3 4 About 95% What proportion of the values are within 3 SDs of the mean (i.e., between 20 and 80 points)? At least 8 9 About 99.7% Observe that the results from the Empirical Rule are consistent with the
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Unformatted text preview: results from Chebyshevs Theorem. The powerful assumption of normality allows us to more precisely pinpoint a proportion, instead of just providing a lower bound, as Chebyshevs Theorem does. In Chapter 6 , we will use a table in Triola to see how we obtain the 68%, 95%, and 99.7% in the Empirical Rule, and we will see how to obtain percents for other cases. For example, what proportion of the values are within 1.5 SDs of the mean?...
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