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# lec7 - STATISTICS 13 STATISTICS Oct 8 2010 Lecture 7 Review...

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STATISTICS 13 STATISTICS 13 STATISTICS 13 Lecture 7 Lecture 7 Oct. 8, 2010 Oct. 8, 2010

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Review Properties of mean and standard deviation Empirical Rule
What does Empirical Rule Tell Us? If data is about Bell shaped, then most of the measurements lie within two standard deviations from their mean Approximation of standard deviation: when data is about bell-shaped, then 4 R s

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Tchebysheff’s Theorem Given n measurements, and an integer k greater than 1, the proportion of measurements that are within k standard deviations from the mean of the measurements is at least 1 – 1/k 2 Applies both for a sample and a population and regardless of the shape of the distribution Example:
Example In 1999, the average time spent online was about 14 hours per person per year. Suppose that the standard deviation of the distribution of x-- the number of hours per person per year spent online, was 20 hours. Questions: - Why do you suppose the yearly average for the entire U.S. population was so low in 1999? -Do you think the distribution is relatively bell- shaped, skewed right, or skewed left? -Within what limits would you expect at least 3/4 of the measurements to lie?

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Example (Cont.) Answers: - Although some people spent a large number of hours per year online, a large majority of the population never used the Internet in 1999.
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lec7 - STATISTICS 13 STATISTICS Oct 8 2010 Lecture 7 Review...

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