# Also the curve is not symmetric at all here are two

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Also the curve is not symmetric at all.

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Here are two histograms, with different bins, of the actual data we are looking at:
Data Set 3 We look at the following data set, describing hypothetical observations of yearly income, in units of \$10,000. The data is sorted to make it easier to identify some indexes 1.008 1.604 4.279 20.416 1.021 1.921 4.422 35.329 1.163 2.409 4.652 40.490 1.389 3.129 5.236 131.974 1.395 3.608 5.892 201.500 1.585 3.899 9.993 1265.355 We also have the following summaries: count 24 sum 1753.667 sum squares 1662727.764 For this data compute (“by hand”, that is, not using a spreadsheet, but calculators are fine) 1. The mean 2. The population variance and population standard deviation 3. The sample variance and sample standard deviation 4. The median 5. The first quartile 6. The third quartile 7. The minimum 8. The maximum 9. The range 10. The midrange Don't draw any conclusion, since we are told nothing about how this data was collected.

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Solutions Here are the answers provided by the same program that generated the data: Mean 73.0694781343654 1 quartile 1.59940776844228 Median 4.08899618485589 3 quartile 12.5983955509013 Population Standard Deviation 252.865922712193 Population Variance 63941.1748690888 Standard Deviation 258.30452173811 Sample Variance 66721.2259503536 Range 1264.34711147247 Minimum 1.00757419406111 Maximum 1265.35468566653 Midrange 633.181129930295 The data was simulated assuming what is called a “Pareto” model. This is one of a category of models that will produce widely scattered data, with ”heavy tails”, that is the histograms should approach zero very slowly. These models have become popular after events like the financial crash of 2007 suggested that “Normal” models were inadequate for the description of markets. In theory, a very large sample should produce a histogram closely resembling the following graph: This is an example of “power law”, since the graph is that of an inverse power (here, proportional to x 3 / 2 ), which approaches 0 much slower than “Normal” (which looks like e x 2 ), or “Exponential” (which looks like e x )
Here are two histograms, with different bins, of the actual data we are looking at: The computer drawn pictures do not quite render the situation: here are the tables listing the bins and their frequency: Table 1 from 1.00757 to below 115.948 21 from 115.948 to below 230.889 2 from 230.889

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• Fall '17

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