Stat Assignment # 2 isa

Assignment #2 Chapter 1 Isabella Laos Displaying distributions with graphs: Homework: #1 + 1.27, 1.29, 1.37, 1.40, 1.42 Exploratory data analysis : use of graphs and numerical summaries to describe variables in a data set and relationships among them Distributions : set of values Bar graphs (categorical data): Represents different categories (favorite fruits in the example to the right) and there is space between the bars of the graph . Pie charts (categorical data) Also represents different categories (preferred pets in the example to the right). Bar charts and pie charts are simply two different ways of graphing categorical data . Histograms (continuous data) In a histogram, different bars represent different range of values . In the chart to the right the number of trees that are 60-65 feet high, 65- 70 feet high and so forth. Notice there is no space between bars in a histogram. Stem-and-leaf plots (continuous data) Another way of graphing continuous data. Stem-and-leaf plots can be either one sided (example to the right) or two sided (our first problem following page). Frequencies : Number of values in each category Symetric: The shape of the distribution above the middle value is identical to the shape of the distribution below the middle value. Skewed: The shape of the distribution above and below the middle value are different—typically indicating more values either above or below the middle value. Outliers : Extreme values. Example: Height in inches: {67, 69, 64, 71, 63, 69, 65, 61, 84 , 68, 62} “84” is an outlier because it is an extreme value much higher than the others. Time plot : Plot values over time. The final problem illustrates this

#1 . Make a 2-sided stem and leaf plot (men to the left, women to the right) that displays the 30 highest heights achieved (in the world) in the high jump for the calendar year 2017. Heights are listed in centimeters. Use the first two digits for each stem and the 3 rd digits as the leaves. Note: smaller values toward the stem, larger values toward the edge. Then answer questions on the following page. Men : 241, 240, 238, 238, 237, 236, 236, 235, 234, 234, 232, 232, 232, 232, 230, 229, 228, 226, 226, 225, 225, 224, 224, 222, 221, 221, 219, 218, 218, 218 Women : 206, 205, 203, 202, 200, 200, 199, 198, 198, 196, 196, 196, 195, 194, 192, 192, 191, 189, 189, 188, 187, 186, 186, 185, 185, 184, 182, 182, 181, 179 Men stem Women 1 0 24 8 8 7 6 6 5 4 4 2 2 2 2 0 23 9 8 6 6 5 5 4 4 2 2 1 1 22 9 8 8 8 21 20 0 0 2 3 5 6 19 1 2 2 1 4 5 6 6 6 8 8 9 18 1 2 2 4 5 5 6 6 7 8 9 9 17 9 What was approximately (estimate, don’t compute) the average height for the top 30 men? (hint, find the middle value) 230 What was approximately the average height for the top 30 women? 192 What obvious conclusion may be drawn about how high the top men jump as compared to the top women? Men jump higher. 1.37. (p. 25) In the box to the left the most popular colors for automobiles are listed. Make a pie chart only to show distribution of most popular colors. Use a ruler and be neat and reasonably accurate. The dotted lines divide the circle into 12.5% segments. 24%  White 19%  Black 16%  Silver 15%  Gray 10%  Red 7%  Blue 5%  Brown 4%  Other 24% 19% 16% 15% 10% 7% 5% 4% Popular Colors white black silver gray red blue brown other

1.40. (p. 25) Make a histogram of IQ points of 7 th graders in a school based on 5-point increments. The chart of IQ values is reproduced on the last sheet of this homework 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 71-75 76-80 81-85 86-90 91-95 96-100 101-105 106-110 111-115 116-120 121-125 126-130 131-135 136-140 Shape of distribution? Approximately normal Outliers? No outliers 1.42. (p. 27) Make a time chart to show the change of winning women’s Boston marathon times from 1972 – 2015. Data are on the last sheet of this handout. Make your marks on the lines. Be as precise as possible. 3:08 (188) 3:04 (184) 3:00 (180) 2:56 (176) 2:52 (172) 2:48 (168) 2:44 (164) 2:40 (160) 2:36 (156) 2:32 (152) 2:28 (148) 2:24 (144) 2:20 (140) 2:16 (136) 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1990 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Is there a general downward trend (suggesting faster times) between 1972 and 2015? Yes there is a general downward trend suggesting faster times between 1972 and 2015. There appears to be a great deal of fluctuation of running times over the 43 years. Why might this fluctuation have occurred? This fluctuation might have occurred because there is more people running now than 43 years ago.

IQ scores of 7 th grade students Boston marathon times (rounded to the nearest minute)) 89 91 97 100 100 102 103 103 104 104 105 106 107 107 108 109 111 111 111 112 113 113 113 114 114 114 115 118 118 119 120 124 127 128 128 128 130 132 136 72 74 77 79 86 90 93 93 96 97 98 102 103 103 103 105 105 106 107 107 110 110 110 111 112 112 112 113 114 115 116 119 119 120 123 123 124 126 127 1972 ‘73 ‘74 ‘75 ‘76 ‘77 ‘78 ‘79 ‘80 ‘81 ‘82 ‘83 ‘84 ‘85 ‘86 ‘87 ‘88 ‘89 ‘90 ‘91 ‘92 ‘93 ‘94 ‘95 ‘96 ‘97 ‘98 ‘99 2000 ‘01 ‘02 ‘03 ‘04 ‘05 ‘06 ‘07 ‘08 ‘09 ‘10 ‘11 ‘12 ‘13 ‘14 ‘15 190 (3:10) 186 (3:06) 167 (2:47) 162 (2:42) 167 (2:47) 168 (2:48) 165 (2:45) 155 (2:35) 154 (2:34) 147 (2:27) 150 (2:30) 143 (2:23) 149 (2:29) 154 (2:34) 145 (2:25) 146 (2:26) 145 (2:25) 144 (2:24) 145 (2:25) 144 (2:24) 144 (2:24) 145 (2:25) 142 (2:22) 145 (2:25) 147 (2:27) 146 (2:26) 143 (2:23) 143 (2:23) 146 (2:26) 144 (2:24) 141 (2:21) 145 (2:25) 144 (2:24) 145 (2:25) 143 (2:23) 149 (2:29) 145 (2:25) 152 (2:32) 146 (2:26) 142 (2:22) 151 (2:31) 146 (2:26) 139 (2:19) 145 (2:25)