Assignment 2 Chapter 1 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 3rd 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 Women 1 0 8 8 7 6 6 5 4 4 2 2 2 2 0 9 8 6 6 5 5 4 4 2 1 1 9 8 8 8 stem 24 23 22 21 20 19 18 17 0 0 2 3 5 6 1 2 2 4 5 6 6 6 8 8 9 1 2 2 4 5 5 6 6 7 8 9 9 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 1 27 1 29 p 24 In the Titanic disaster 1912 the number of people on board in each of the three classes are listed Next to that value are listed the number saved in each class Create a bar chart to identify the number on board and the number saved in each of the three classes First class Second class 277 on board Third class 709 on board 200 saved 119 saved 181 saved 323 Passengers on board 740 700 660 620 580 540 500 460 420 380 340 300 260 220 180 140 100 60 20 1st class 1st class saved 2nd class 2nd class saved 3rd class 3rd class saved total Based on this chart does it appear that favoritism was shown to first class passengers Yes total total Based on your knowledge of the Titanic disaster do you believe that you would find a difference in the proportion of males saved and the proportion of females saved Not equal proportions More women were saved because the rules at that time were women first 1 40 p 25 Make a histogram of IQ points of 7th 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 0 136 140 131 135 81 85 86 90 91 95 96 100 101 105 106 110 111 115 116 120 121 125 126 130 71 75 76 80 Shape of distribution Approximately normal Outliers NO 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 1 9 7 2 1 9 7 3 1 9 7 4 1 9 7 5 1 9 7 6 1 9 7 7 1 9 7 8 1 9 7 9 1 9 8 0 1 9 8 1 1 9 8 2 1 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 0 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 Is there a general downward trend suggesting faster times between 1972 and 2015 There is an extreme drop in the times from 1972 to 1975 There is a moderate drop in times from 1976 to 1983 In 1984 to 1985 there is a more drastic change in times but then from 1986 until 2006 the times become more steady From 2007 to 2015 there is a moderate fluxation of times There appears …