# Data set 2 we look at the following data set

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Data Set 2 We look at the following data set, describing very hypothetical observations of interarrival times of a bus at a bus stop. The data is sorted to make it easier to identify some indexes 0.1 2.5 8.3 28.6 0.3 2.7 9.1 29.0 0.9 3.0 11.6 33.6 1.2 3.2 12.4 41.6 1.3 3.6 13.5 45.0 1.6 3.9 15.0 46.6 1.7 4.2 18.0 49.5 1.7 4.5 18.7 71.9 2.3 4.6 21.2 92.2 2.5 6.5 21.5 115.0 We also have the following summaries: Count 40 Sum 754.7 Sum of squares 40684.6 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 18.8662545343612 1 quartile 2.51121900937518 Median 7.38373031601704 3 quartile 23.2795020742005 Population Standard Deviation 25.7134102638779 Population Variance 661.179467398501 Sample Standard Deviation 26.0409828362023 Sample Variance 678.132787075385 Range 114.906089411266 Minimum 0.12702396574074 Maximum 115.033113377007 Midrange 57.580068671374 The data was simulated assuming what is called an “Exponential” model. This model fits interarrival times of events that are completely unconnected – typically, requests for service to a common resource (like a printer) in a vast network, or, as its original application, phone calls arriving at a central city switchboard (at the time when these things existed) In theory, a very large sample should produce a histogram closely resembling the following graph: Notice how the “tail” (the left end of the graph) approaches 0 at a slower pace than the preceding (“Normal”) picture.
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