However are affected by outliers and would change if

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however, are affected by outliers and would change if there were a year with 30 hurricanes. The further away the outlier, the more it will affect the mean and standard deviation. Mean and standard deviation are measures which are not resistant to outliers. Practice Exercise (p. 10) 1. Describe the distribution. The distribution appears unimodal and somewhat symmetrical. The spread is from about $60,000 to $150,000 and the center is around $100,000. We can say that the typical claim is around $100,000 with a minimum claim of $60,000 and maximum of $150,000. There don’t appear to be any major outliers although the maximum claim of $150,000 is the highest by about $30,000. 2. Compute the median, mean, and standard deviation. The table below may help in computing the standard deviation. The mean of the distribution is 98.8 and the standard deviation is 21.33. The table that will aid students in computing the standard deviation is shown below: Claims Claim - Mean (Claim - Mean)^2 112 13.2 174.24 92 -6.8 46.24 99 0.2 0.04 90 -8.8 77.44 117 18.2 331.24 79 -19.8 392.04 141 42.2 1780.84 66 -32.8 1075.84 86 -12.8 163.84 106 7.2 51.84 SUM 4093.6 The sum divided by 9 is 454.84 and the square root of this is the standard deviation of 21.33.
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MODULE 1 Page 8 3. What percentage of claims in the data set are (a) within 1 standard deviation of the mean (that is, from the mean minus the standard deviation to the mean plus the standard deviation); (b) within 2 standard deviations of the mean; and (c) within 3 standard deviations of the mean? a. 1 std dev is from 77.5 to 120.1 = 80%, b. 2 std dev is from 56.3 to 141.4 = 100%, c. 3 std dev = 100% 4. Create a dot plot showing these claims. 5. Describe the distribution. Mean = 1.1; std dev = 1.73 6. What percentage of claims in the data set are (a) within 1 standard deviation of the mean; (b) within 2 standard deviations of the mean; (c) within 3 standard deviations of the mean? 80% are within 1 std dev, 90% are within 2 std devs, and 100% are within 3 std devs 7. What are the main differences between the distributions of claims from homes farther down the beach and the one of claims from homes right on the beach? Clearly, claims are much lower for these 10 homes. Variability is also much smaller. The shape of this distribution is skewed right. 7 out of the 10 homes do not even have any claims. This tells us that homes on the beach are at much greater risk for damage in a Category 3 hurricane. MODULE 1
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MODULE 2 Page 9 Module 2: The Normal Model In this module students will learn about standardizing a distribution and about a particularly useful distribution, the normal model. Content Learning Objectives Through the analysis of actual historical hurricane data and data from the fictional town of Happy Shores, students will be able to do the following: ± Compute z-scores (number of standard deviations from mean) in order to standardize values from a distribution. ± Understand when it is appropriate (and not appropriate) to use the normal model to represent real world data.
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