- Exercise 1.25 (1 Point):
Table 1.3 contains the percent of residents 65 years of age and over in each of the 50 states.
(a) Make a stemplot of these data using percent as stems and tenths of a percent as leaves. Then make a second stemplot splitting each stem in two (for leaves 0 to 4 and leaves 5 to 9). Which display do you prefer?
(b) Describe the shape, center, and spread of the distribution. Is it roughly symmetric or distinctly skewed? Which states are clear outliers? Use what you know about the states to explain these outliers.Table 1.3 Percent of population 65 years old and over, by state (1995)State Percent State Percent State Percent Alabama 13.0 Louisiana 11.4 Ohio 13.4 Alaska 4.9 Maine 13.9 Oklahoma 13.5 Arizona 13.3 Maryland 11.3 Oregon 13.6 Arkansas 14.5 Massachusetts 14.2 Pennsylvania 15.9 California 11.0 Michigan 12.4 Rhode Island 15.7 Colorado 10.0 Minnesota 12.4 South Carolina 12.0 Connecticut 14.3 Mississippi 12.3 South Dakota 14.4 Delaware 12.6 Missouri 13.9 Tennessee 12.5 Florida 18.6 Montana 13.1 Texas 10.2 Georgia 10.0 Nebraska 13.9 Utah 8.8 Hawaii 12.6 Nevada 11.4 Vermont 12.0 Idaho 11.4 New Hampshire 11.9 Virginia 11.1 Illinois 12.5 New Jersey 13.7 Washington 11.6 Indiana 12.6 New Mexico 10.9 West Virginia 15.3 Iowa 15.2 New York 13.4 Wisconsin 13.3 Kansas 13.7 North Carolina 12.5 Wyoming 11.1 Kentucky 12.6 North Dakota 14.5 Source: Statistical Abstract of the United States, 1996.
- Exercise 1.29 (1 Point):
Make a graph of the distribution of IQ scores for the seventh-grade students in Table 1.6. Describe the shape, center, and spread of the distribution, as well as any outliers. IQ scores are usually said to be centered at 100. Is the midpoint for these students close to 100, clearly above, or clearly below?Table 1.6 Educational data for 78 seventh-grade studentsOBS GPA IQ Gender Self concept 001 7.940 111 M 67 002 8.292 107 M 43 003 4.643 100 M 52 004 7.470 107 M 66 005 8.882 114 F 58 006 7.585 115 M 51 007 7.650 111 M 71 008 2.412 97 M 51 009 6.000 100 F 49 010 8.833 112 M 51 011 7.470 104 F 35 012 5.528 89 F 54 013 7.167 104 M 54 014 7.571 102 F 64 015 4.700 91 F 56 016 8.167 114 F 69 017 7.822 114 F 55 018 7.598 103 F 65 019 4.000 106 M 40 020 6.231 105 F 66 021 7.643 113 M 55 022 1.760 109 M 20 024 6.419 108 F 56 026 9.648 113 M 68 027 10.700 130 F 69 028 10.580 128 M 70 029 9.429 128 M 80 030 8.000 118 M 53 031 9.585 113 M 65 032 9.571 120 F 67 033 8.998 132 F 62 034 8.333 111 F 39 035 8.175 124 M 71 036 8.000 127 M 59 037 9.333 128 F 60 038 9.500 136 M 64 039 9.167 106 M 71 040 10.140 118 F 72 041 9.999 119 F 54 Table 1.6 continued Educational data for 78 seventh-grade studentsOBS GPA IQ Gender Self concept 043 10.760 123 M 64 044 9.763 124 M 58 045 9.410 126 M 70 046 9.167 116 M 72 047 9.348 127 M 70 048 8.167 119 M 47 050 3.647 97 M 52 051 3.408 86 F 46 052 3.936 102 M 66 053 7.167 110 M 67 054 7.647 120 M 63 055 0.530 103 M 53 056 6.173 115 M 67 057 7.295 93 M 61 058 7.295 72 F 54 059 8.938 111 F 60 060 7.882 103 F 60 061 8.353 123 M 63 062 5.062 79 M 30 063 8.175 119 M 54 064 8.235 110 M 66 065 7.588 110 M 44 068 7.647 107 M 49 069 5.237 74 F 44 071 7.825 105 M 67 072 7.333 112 F 64 074 9.167 105 M 73 076 7.996 110 M 59 077 8.714 107 F 37 078 7.833 103 F 63 079 4.885 77 M 36 080 7.998 98 F 64 083 3.820 90 M 42 084 5.936 96 F 28 085 9.000 112 F 60 086 9.500 112 F 70 087 6.057 114 M 51 088 6.057 93 F 21 089 6.938 106 M 56
- Exercise 1.43 (3 Points):
Here are the scores on the Survey of Study Habits and Attitudes (SSHA) for 18 first-year college women:and for 20 first-year college men:154 109 137 115 152 140 154 178 101 103 126 126 137 165 165 129 200 148 (a) Make a back-to-back stemplot of these data, or use your result from Exercise 1.20.108 140 114 91 180 115 126 92 169 146 109 132 75 88 113 151 70 115 187 104
(b) Find the mean and the median for both sets of SSHA scores. What feature of each distribution explains the fact that the mean is larger than the median?
(c) Find the five-number summaries for both sets of SSHA scores. Your plot in (a) suggests that there is an outlier among the women's scores. Does the 1.5 x IQR criterion flag this observation? Make side-by-side boxplots for the two distributions. (Be sure to use a common scale to make comparison easy.)
(d) Use your results to write a brief comparison of the two groups. Do women as a group score higher than men? Which of your descriptions (stemplots, boxplots, numerical measures) show this? Which group of scores is more spread out when we ignore outliers? Which of your descriptions shows this most clearly?
Many more designs and examples for micromaps exist. Several articles on micromaps have been published in the Statistical Computing and Statistical Graphics Newsletter by Carr et al., e.g., in Vol. 7, No. 3, pp. 16-23, and Vol. 9, No. 1, pp. 24-32. Actually, the micromaps with the CO2 data and the wheat data are Figures 1 and 2 of the Carr et al. article in Vol. 9, No. 1.
The Statistical Computing and Statistical Graphics Newsletter is accessible at http://cm.bell-labs.com/cm/ms/who/cocteau/newsletter/index.html and provides access to complete issues as pdf and postscript files. It is informative and easy to read.
Here are three more micromaps for Iowa, Michigan, and Pennsylvania. Select one of these three maps and carefully describe and interpret it (about one half page up to one page). Use all your geographical knowledge (e.g., where are big cities, sparsely populated rural areas, what is happening in counties just outside the visible area) and technical knowledge (where do benzene and lead originate from? - note that the data for Michigan is an aggregation of 148 HAPs with lead and benzene as major components). Also note that the data is from 1990. (6 Points)
- a) (i) If you were the governor of New York, which graphic would
you use to demonstrate how advanced your state is?
(ii) If you were the governor of Connecticut, which graphic would you use to demonstrate how advanced your state is?
(iii) If you were the governor of New Jersey, which graphic would you use to demonstrate how advanced your state is?
(iv) If you were the governor of Virginia, which graphic would you use to demonstrate how far behind your state is and desperately needs federal funding?
(v) If you were a historician who wants to show how few telephones were around in 1960, which graphic would you use?
- b) Now find the "true" interval for the following 5 states.
Do this by calculating the intersection of the class intervals used within
the 4 graphics above:
Maine
New York
Connecticut
New Jersey
Virginia
- c) Describe your findings from b) in one or two sentences.
- d) Now think of micromaps. Can you manipulate these as easily as these maps to express different political opinions? Explain. Describe how a micromap of this data might look like.
Unfortunately, the small print got lost when scanning in these graphics.
In the upper graphic, the lines under "Fuel Economy..." read "Set by Congress and supplemented by the Transportation Department. In Miles per gallon".
In the middle graphic, the text at the 4 markers in the upper right part reads: "Jan 1, 5% increase", "April 1, 3.809% increase", "July 1, 2.294% increase", and "Oct. 1, 2.691% increase". The Dollar amounts given underneath are "$13.34", "$13.84", "$14.16", and "$14.54". The labels at the bottom under "1979" read "Jan to March", "April to June", "July to Sept.", and "Oct to Dec".
In the bottom graphic, it should read "1972 = 100".