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Unformatted text preview: 1 Ron_Knapp1.doc WEEK 1 HOMEWORK - CH3 P3-65. U.S. housing prices reached their peak in July of 2006. The following data shows the ratio of the prices reported in a recent month to the July 2006 figure. These are to be used to represent typical amounts of decline from that peak for 20 cities. Phoenix Los Angeles San Diego San Franciso Denver Washington Miami Tampa Atlanta Chicago 0.760 0.784 0.764 0.802 0.909 0.828 0.786 0.792 0.933 0.915 Boston Detroit Minneapolis Charlotte Las Vegas New York Cleveland Portland Dallas Seattle 0.902 0.792 0.855 1.025 0.756 0.922 0.865 0.981 0.939 0.999 a. Find the mean, median, and mode of these statistics. The mean of a set or average is calculated by adding up all the numbers in the set, and dividing that sum by the number of entries. 0.760+0.784+0.764+0.802+0.909+0.828+0.786+0.792+0.933+0.915+0.902+0.792+0.855+1.025+0.756+0.922 +0.865+0.981+0.939+0.999=17.309 \ 20 = 0.86545 The mean is 0.8654 The median of a set is another way of calculating a sort of middle value for a data set. In fact, the median is the actually the middle number when you put the data in order. If you get two middle numbers (because you have an even number of data points) just take their average. See below: 0.756+0.760+0.764+0.784+0.786+0.792+0.792+0.802+0.828+ 0.855 + 0.865 +0.902+0.909+0.915+0.922+0.933 +0.939+0.981+0.999+1.025 0.855+0.865=1.72 \ 2 = 0.86 The median is 0.86 The mode is the number that occurs most frequently in a data set. Sometimes a set can have more than one mode. 0.756+0.760+0.764+0.784+0.786+ 0.792 + 0.792 +0.802+0.828+0.855+0.865+0.902+0.909+0.915+0.922+0.933 +0.939+0.981+0.999+1.025 The mode is 0.792 b. What are the range and standard deviation of the values? (Assume this to be sample information.) The range of a set is the difference between the highest and lowest values. The range of scores for our housing prices is 1.025 0.756 = 0.269 0.756 +0.760+0.764+0.784+0.786+0.792+0.792+0.802+0.828+0.855+0.865+0.902+0.909+0.915+0.922+0.933 +0.939+0.981+0.999+ 1.025 Standard deviation is a measure of how spread out the data points are. A set with a low standard deviation (SD) has most of the data points centered around the average. A set with a high SD has data points that are not so clustered around the average. First we calculate the difference between each data point and the average. Then square those numbers, then add them up and divide by either n-1 or n. You divide by n-1 when your data set is a sample larger set, and you divide by n when your data set is the whole set. Ours is sample of a larger set, see below: X 0.756+0.760+0.764+0.784+0.786+0.792+0.792+0.802+0.828+0.855+0.865+0.902+0.909+0.915+0.922+0.933 +0.939+0.981+0.999+1.025=17.309000 M 0.865450 (X-M)-0.109450+-0.105450+-0.101450+-0.81450+-0.079450+-0.073450+-0.073450+-0.063450+-0.037450+ -0.010450+-0.000450+0.036550+0.043550+0.049550+0.056550+0.067550+0.073550+0.115550+ 0.133550+0.159550=0.000000 2 Ron_Knapp1.doc (X-M) ^ 2 0.011979+0.011120+0.010292+0.006634+0.006312+0.005395+0.005395+0.004026+0.001403+ 0....
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- Fall '10