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Chapter 2: Graphical Descriptions of Data TECHNOLOGY: ENTERING OR UPLOADING DATA INTO STATCRUNCH Entering your own data that you do not have in a file:  Go to Statcrunch.com and login.  Click “Open StatCrunch”. A spreadsheet will open where you can rename the columns using the variable names for your data. You can then enter the raw data into the columns. Entering data from a file:  For the examples and homework problems in this book, you have a file in Blackboard called “Chapter 2 Data”. Save that file to your desktop.  Go to Statcrunch.com and login.  Click “MyStatCrunch”. Under “My Data”, click “Select a file from my computer”. Then choose the file you just saved to your desktop.  Then scroll down and click “Load file” and you will see the data automatically load into the columns of the spreadsheet.  This file is automatically saved under “My Data”. So the next time you login to StatCrunch, you can click “MyStatCrunch” and then click “My Data” and this file will be in the list to choose. TECHNOLOGY: FREQUENCY AND RELATIVE FREQUENCY TABLES IN STATCRUNCH  Enter the data into a column in the spreadsheet (see earlier instructions on entering a list of data)  Click Stat, Tables, Frequency  In the popup window that opens, choose the variable name from “Select Columns”  Under “Statistics” Frequency and Relative Frequency are already chosen so you do not need to click anything there.  Under “Order by” you can choose “Values ascending” to put the categories in ABC order in the table, or “Count ascending” to put the categories in order by frequency, or “Worksheet” to put the categories in order of appearance in the column of data.  Under “”Other*” if percent less than” you can enter a number like 10 to put all categories with less than 10% into a combined category called “Other*”  Then click “Compute!” 24

Chapter 2: Graphical Descriptions of Data Some key features of a bar graph:  Equal spacing on each axis.  Bars are the same width.  There should be labels on each axis and a title for the graph.  There should be an equal scaling on the frequency/relative frequency axis and the categories should be listed on the category axis.  The bars don’t touch. You can also draw a bar graph using relative frequency on the vertical axis. This is useful when you want to compare two samples with different sample sizes. The relative frequency graph and the frequency graph should look the same, except for the scaling on the frequency axis. If you follow the StatCrunch directions above for the list of data called “Car Data” in the “Chapter02DataFile” you will get the following relative frequency bar chart (value ascending and any category with less than 10% was put into an “Other*” category): Graph #2.1.2: Relative Frequency Bar Chart for Type of Car Data If instead you had chosen “Count descending” the bar plot would look as follows: 27

Chapter 2: Graphical Descriptions of Data If you follow the StatCrunch directions above for the list of raw data called “Car Data” in the “Chapter02DataFile” you will get the following pie chart (value ascending and any category with less than 10% was put into an “Other*” category): Graph #2.1.3: Pie Chart for Type of Car Data As you can see from the graph, Toyota and Chevy are more popular, while the cars in the other category are liked the least. Of the cars that you can determine from the graph, Ford is liked less than the others. TECHNOLOGY: PIE CHARTS (PIE GRAPHS) FROM GROUPED DATA Using StatCrunch :  Enter the data into a column in the spreadsheet (see earlier instructions on entering a list of data)  Click Graph, Pie Chart, With Summary  In the popup window that opens choose the variable name from “Categories In” and the column with the counts from “Counts in”  The rest of the steps are the same as for raw data (except don’t put anything next to “Other if percent less than”). If instead you had been given the grouped data from the start (instead of the list of 50 data points), you could have made the pie chart using the grouped data instead as follows: In StatCrunch open the data file called “Chapter02DataFile”. You will see two lists that look as follows: 30

Chapter 2: Graphical Descriptions of Data Example #2.1.4: Side-By-Side Bar Chart In a city with a maximum-security prison, the residents have been polled to determine if a relationship exists between marital status and a resident's stand on capital punishment. The results are cross-classified into the following contingency table. Make a side-by-side bar chart. Stand on Capital Marital Status Punishment Married Not Married Total Favor 100 20 120 Oppose 50 30 80 Total 150 50 200 Enter the contingency table above into StatCrunch and then make a side-by-side and segmented bar chart grouped by “Stand on Capital Punishment”. The data would look as follows in StatCrunch: Following the directions from the technology box on the previous page you would get the following: Graph #2.1.4: Side-By-Side and Segmented Bar Charts for Stand on Capital Punishment Data: (Vertical bars (split)) (Vertical bars (stacked)) We usually prefer the graphs with vertical bars, but you can also make them with horizontal bars. 33

Chapter 2: Graphical Descriptions of Data 6.) People in Bangladesh were asked to state what type of birth control method they use. The percentages are given in table #2.1.9 ("Contraceptive use," 2013). Create a Pareto chart of the data (bar chart with “Count descending”) and then state any findings you can from the graph. Table #2.1.9: Data of Birth Control Type Method Percentage Condom 4.50% Pill 28.50% Periodic Abstinence 4.90% Injection 7.00% Female Sterilization 5.00% IUD 0.90% Male Sterilization 0.70% Withdrawal 2.90% Other Modern Methods 0.70% Other Traditional Methods 0.60% None 44.3% 7.) In a study of 478 fourth, fifth and sixth graders, the following data were collected on their gender and on their primary goal. Make a side-by-side and segmented bar chart with the data grouped by gender. Good Grades Popularity Good at Sports Total Male 117 50 60 227 Female 130 91 30 251 Total 247 141 90 478 36

Chapter 2: Graphical Descriptions of Data Table #2.2.2: Frequency Distribution for Monthly Rent Class Boundaries  Tally  Frequency Relative Frequency 349.5 – 664.5    4 0.17 664.5 – 979.5 8 0.33 979.5 – 1294.5    5 0.21 1294.5 – 1609.5   6 0.25 1609.5 – 1924.5    0 0 1924.5 – 2239.5  0 0 2239.5 – 2554.5     1 0.04 TOTAL 24 1.00 It is difficult to determine the basic shape of the distribution by looking at the frequency distribution. It would be easier to look at a graph. The graph of a frequency distribution for quantitative data is called a histogram . Histogram – a graph of the frequencies (or relative frequencies) on the vertical axis and the class boundaries (or class midpoints) on the horizontal axis. Rectangles where the height is the frequency (or relative frequency) and the width is the class width are draw for each class. TECHNOLOGY: HISTOGRAMS Using StatCrunch :  Enter the data into a column in the spreadsheet (see earlier instructions on entering a list of data)  Click Graph, Histogram  In the popup window that opens choose the variable name from “Select Columns”  Under “Type” choose Frequency or Relative Frequency depending on what you have been asked for.  Under “Bins” start the bins at the lowest class boundary and use the class width as the bin width.  Under “Graph properties” you can give your graph a title.  Then click “Compute!” Example #2.2.2: Drawing a Histogram Draw a histogram for the distribution from example #2.2.1. Solution: The class boundaries are plotted on the horizontal axis and the frequencies are plotted on the vertical axis. In StatCrunch click on My Data and then click Chapter02DataFile. Follow the directions above using the column called “Monthly Rent”. Under “Type” you want to choose Frequency. Also from the earlier example we computed the first lower class boundary to be 349.5 and the class width to be 315. These are used for where we start the bins at and for the bin width respectively. 39

Chapter 2: Graphical Descriptions of Data Draw a relative frequency histogram for the monthly rent distribution from example #2.2.1. Solution: The class boundaries are plotted on the horizontal axis and the relative frequencies are plotted on the vertical axis. In StatCrunch click on My Data and then click Chapter02DataFile. Follow the directions above using the column called “Monthly Rent”. Under “Type” you want to choose Relative Frequency. Also from the earlier example we computed the first lower class boundary to be 349.5 and the class width to be 315. These are used for where we start the bins at and for the bin width respectively. Graph #2.2.2: Relative Frequency Histogram for Monthly Rent Notice the shape of the relative frequency distribution is the same as the shape of the frequency distribution. The only difference is that the vertical axis now has relative frequencies instead of frequencies. Shapes of the distribution: 42

Chapter 2: Graphical Descriptions of Data The point of this chapter is not just to be able to MAKE a frequency table or a graph of the data. One of the characteristics we will be interested in later is the SHAPE of the distribution. Before drawing inferences using the results of a set of sample data, often you need to first look at the histogram and look at three things: shape, center and spread. We will discuss shape here and we will discuss measures of center and spread in the next chapter. Below are some of the common distribution shapes we will see this semester. bell-shaped (symmetric) uniform (symmetric) right-skewed (not symmetric) left-skewed (not symmetric) Some shapes are symmetric and some are not. Symmetric means that you can fold the graph in half down the middle and the two sides will line up. You can think of the two sides as being mirror images of each other. Skewed means one “tail” of the graph is longer than the other. The graph is skewed in the direction of the longer tail. Another interest is how many peaks a graph may have. Modal refers to the number of peaks. Unimodal has one peak and bimodal has two peaks. Usually if a graph has more than two peaks, the modal information is no longer of interest. Other important features to consider are gaps between bars, a repetitive pattern, how spread out the data are, and where the center of the graph is. Examples of graphs: Graph #2.2.6: Symmetric, Unimodal Graph Graph #2.2.7: Symmetric, Bimodal Graph 43

Chapter 2: Graphical Descriptions of Data Graph #2.2.8: Skewed Right Graph Graph #2.2.9: Skewed Left Graph with a Gap Graph #2.2.10: Uniform Graph Example #2.2.7: Creating a Frequency Distribution and Histogram 44

Chapter 2: Graphical Descriptions of Data The following data represent the percent change in tuition levels at public, four- year colleges (inflation adjusted) from 2008 to 2013 (Weissmann, 2013). Create a frequency distribution and histogram for the data using 8 classes. Table #2.2.5: Data of Tuition Levels at Public, Four-Year Colleges 19.5% 40.8% 57.0% 15.1% 17.4% 5.2% 13.0% 15.6% 51.5% 15.6% 14.5% 22.4% 19.5% 31.3% 21.7% 27.0% 13.1% 26.8% 24.3% 38.0% 21.1% 9.3% 46.7% 14.5% 78.4% 67.3% 21.1% 22.4% 5.3% 17.3% 17.5% 36.6% 72.0% 63.2% 15.1% 2.2% 17.5% 36.7% 2.8% 16.2% 20.5% 17.8% 30.1% 63.6% 17.8% 23.2% 25.3% 21.4% 28.5% 9.4% Solution: First identify the individual, variable and type of variable. Individual: Variable: Type of variable: 1) Compute the class width: ( largestdata value − smallest data value ) number of classes = ¿ Since the data values have one decimal place, round this up to the next tenth number. So the class width = 9.6 2) Compute the lowest class boundary: Since the data are tenths numbers, Lowest class boundary = smallest data value – 0.05 = 3) Create the classes. The lower class boundaries start at 2.15 and you keep adding 9.6 down The upper class boundaries start at 11.75 and you keep adding 9.6 down Class Boundaries Tally Frequency 2.15 – 11.75 11.75 – 21.35 21.35 – 30.95 30.95 – 40.55 40.55 – 50.15 50.15 – 59.75 59.75 – 69.35 69.35 – 78.95  Here we now have 8 classes which is what was asked for and the largest data value of 78.4 is contained in the last class. 4) Tally and find the frequency of the data: 45

Chapter 2: Graphical Descriptions of Data Go through the data and put a tally mark in the appropriate class for each piece of data by looking to see which class boundaries the data value is between. Fill in the frequency by changing each of the tallies into a number. Table #2.2.6: Frequency Distribution for Tuition Levels at Public, Four-Year Colleges Class Boundaries Tally Frequency 2.15 – 11.75   11.75 – 21.35 21.35 – 30.95   30.95 – 40.55   40.55 – 50.15 50.15 – 59.75 59.75 – 69.35   69.35 – 78.95 Make sure the total of the frequencies is the same as the number of data points. To make the frequency histogram, the class boundaries are plotted on the horizontal axis and the frequencies are plotted on the vertical axis. In StatCrunch click on My Data and then click Chapter02DataFile. Follow the directions above using the column called “Tuition Change”. Under “Type” you want to choose Frequency. The lowest class boundary was 2.15 and the class width was 9.6. These are used for where we start the bins and for the bin width respectively. You can also check the box next to “value above the bar” to get the count for each class. Graph #2.2.11: Histogram for Tuition Levels at Public, Four-Year Colleges 46

Chapter 2: Graphical Descriptions of Data If you want your x-axis to have the class boundaries on the sides of the bars instead of the numbers above, click on down in the lower left corner of the graph and then pick X-axis. Next to “Tick marks” enter the list of class boundaries from your frequency table separated by commas as shown below: When you click , your graph will now look as follows: This graph is skewed right, with no gaps. This says that the most frequent percent increases in tuition were between 11.75% and 21.35%. 47

Chapter 2: Graphical Descriptions of Data There are other types of graphs for quantitative data. They will be explored in the next section. Section 2.2: Homework 1.) The median incomes of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #2.2.9 ("Median income of," 2013). Create a frequency distribution and a relative frequency distribution using 7 classes. Table #2.2.9: Data of Median Income for Males $42,951 $52,379 $42,544 $37,488 $49,281 $50,987 $60,705 $50,411 $66,760 $40,951 $43,902 $45,494 $41,528 $50,746 $45,183 $43,624 $43,993 $41,612 $46,313 $43,944 $56,708 $60,264 $50,053 $50,580 $40,202 $43,146 $41,635 $42,182 $41,803 $53,033 $60,568 $41,037 $50,388 $41,950 $44,660 $46,176 $41,420 $45,976 $47,956 $22,529 $48,842 $41,464 $40,285 $41,309 $43,160 $47,573 $44,057 $52,805 $53,046 $42,125 $46,214 $51,630 2.) The median incomes of females in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #2.2.10 ("Median income of," 2013). Create a frequency distribution and a relative frequency distribution using 7 classes. Table #2.2.10: Data of Median Income for Females $31,862 $40,550 $36,048 $30,752 $41,817 $40,236 $47,476 $40,500 $60,332 $33,823 $35,438 $37,242 $31,238 $39,150 $34,023 $33,745 $33,269 $32,684 $31,844 $34,599 $48,748 $46,185 $36,931 $40,416 $29,548 $33,865 $31,067 $33,424 $35,484 $41,021 $47,155 $32,316 $42,113 $33,459 $32,462 $35,746 $31,274 $36,027 $37,089 $22,117 $41,412 $31,330 $31,329 $33,184 $35,301 $32,843 $38,177 $40,969 $40,993 $29,688 $35,890 $34,381 3.) The density of people per square kilometer for African countries is in table #2.2.11 ("Density of people," 2013). Create a frequency distribution and a relative frequency distribution using 8 classes. Table #2.2.11: Data of Density of People per Square Kilometer 15 16 81 3 62 367 42 123 8 9 337 12 29 70 39 83 26 51 79 6 157 105 42 45 72 72 37 4 36 134 12 3 630 563 72 29 3 13 176 341 415 187 65 194 75 16 41 18 69 49 103 65 143 2 18 31 48

Chapter 2: Graphical Descriptions of Data 4.) The Affordable Care Act created a market place for individuals to purchase health care plans. In 2014, the premiums for a random sample of 36 twenty-seven year olds signed up for the bronze level health insurance are given in table #2.2.12 ("Health insurance marketplace," 2013). Create a frequency distribution and a relative frequency distribution using 5 classes. Table #2.2.12: Data of Health Insurance Premiums $114 $119 $121 $125 $132 $139 $139 $141 $143 $145 $151 $153 $156 $159 $162 $163 $165 $166 $170 $170 $176 $177 $181 $185 $185 $186 $186 $189 $190 $192 $196 $203 $204 $219 $254 $286 5.) Create a histogram and relative frequency histogram for the data in table #2.2.9. Describe the shape and any findings you can from the graph. 6.) Create a histogram and relative frequency histogram for the data in table #2.2.10. Describe the shape and any findings you can from the graph. 7.) Create a histogram and relative frequency histogram for the data in table #2.2.11. Describe the shape and any findings you can from the graph. 8.) Create a histogram and relative frequency histogram for the data in table #2.2.12. Describe the shape and any findings you can from the graph. 9.) Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution and histogram for the data using a lower class limit of 59.5 and a class width of 10. Describe the shape of the distribution. Table #2.2.13: Data of Test 1 Grades 80 79 89 74 73 67 79 93 70 70 76 88 83 73 81 79 80 85 79 80 79 58 93 94 74 10.) Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution and histogram for the data using a lower class limit of 59.5 and a class width of 10. Describe the shape of the distribution. Compare to the graph in question 9. Table #2.2.14: Data of Test 1 Grades 67 67 76 47 85 70 87 76 80 72 84 98 84 64 65 82 81 81 88 74 87 83 49

Chapter 2: Graphical Descriptions of Data Section 2.3: Other Graphical Representations of Data There are many other types of graphs. The following is a description of the stem-and-leaf plot and the scatter plot. Stem-and-Leaf Plots Stem-and-leaf plots are a quick and easy way to look at small samples of numerical data. You can look for any patterns or any strange data values. It is easy to compare two samples using stem plots. The first step is to divide each number into 2 parts, the stem (such as the leftmost digit) and the leaf (such as the rightmost digit). There are no set rules, you just have to look at the data and see what makes sense. Example #2.3.1: Stem-and-Leaf Plot for Grade Distribution The following are the percentage grades of 25 students from a statistics course. Draw a stem-and-leaf plot of the data. Table #2.3.1: Data of Test Grades 62 87 81 69 87 62 45 95 76 76 62 71 65 67 72 80 40 77 87 58 84 73 93 64 89 Solution: First identify the individual, variables and type of variables. Individual: Variable: Type of variable: Make a vertical chart with the stems on the left of a vertical bar. Be sure to fill in any missing stems. In other words, the stems should have equal spacing (for example, count by ones or count by tens). The graph #2.3.1 shows the stems for this example. Graph #2.3.1: Stem-and-Leaf plot for Test Grades Step 1 4 5 6 7 8 9 Now go through the list of data and add the leaves. Put each leaf next to its corresponding stem. Don’t worry about order yet just get all the leaves down. 50

Chapter 2: Graphical Descriptions of Data When the data value 62 is placed on the plot it looks like the plot in graph #2.3.2. Graph #2.3.2: Stem-and-Leaf for Test Grades Step 2 4 5 6 7 8 9 When the data value 87 is placed on the plot it looks like the plot in graph #2.3.3. Graph #2.3.3: Stem-and-Leaf for Test Grades Step 3 4 5 6 7 8 9 Filling in the rest of the leaves to obtain the plot in graph #2.3.4. Graph #2.3.4: Stem-and-Leaf for Test Grades Step 4 4 5 0 5 8 6 2 9 2 2 5 7 4 7 6 6 1 2 7 3 8 7 1 7 0 7 4 9 9 5 3 Now you have to add labels and make the graph look pretty. You need to add a label and sort the leaves into increasing order. You also need to tell people what the stems and leaves mean by inserting a legend. Be careful to line the leaves up in columns. You need to be able to compare the lengths of the rows when you interpret the graph. The final stem plot for the test grade data is in graph #2.3.5. 51

Chapter 2: Graphical Descriptions of Data Graph #2.3.5: Stem-and-Leaf for Test Grades Test Scores 4 0 = 40% 4 0 5 5 8 6 2 2 2 4 5 7 9 7 1 2 3 6 6 7 8 0 1 4 7 7 7 9 9 3 5 Now you can interpret the stem-and-leaf display. The data is bimodal and somewhat symmetric. There are no gaps in the data. The center of the distribution is around 70. TECHNOLOGY: STEM-AND-LEAF PLOT Using StatCrunch :  Enter the data into a column in the spreadsheet (see earlier instructions on entering a list of data)  Click Graph, Stem and Leaf  In the popup window that opens choose the variable name from “Select Columns”  Under “Leaf Unit” choose the place value that will be in the leaf (for example if the data set has 2-digit whole numbers, the number in the ones place would be the leaf so you would choose “1” from the drop-down list).  Under “Outlier trimming” choose None.  Then click “Compute!” If you follow the above directions to use StatCrunch to make the stem-and-leaf plot for the data in Example #2.3.1, you would get the following: Notice that StatCrunch will split all of the stems into two stems if there are too many leaves for a given stem. Scatter Plot 52

Chapter 2: Graphical Descriptions of Data Sometimes you have two different quantitative variables and you want to see if they are related in any way. A scatter plot helps you to see what the relationship would look like. A scatter plot is just a plotting of the ordered pairs. TECHNOLOGY: SCATTERPLOT Using StatCrunch :  Enter the data into a column in the spreadsheet (see earlier instructions on entering a list of data)  Click Graph, Scatter Plot  In the popup window that opens choose the X Variable and Y Variable from the drop-down menus  Under “Graph properties” you can put a title  Then click “Compute!” Using your TI84 :  First push STAT 1 and enter the data into L1 and L2  Push 2 nd Y= to open the STAT PLOTS menu. Then push 1 to select Plot1  You need to make your input screen look like the screen below (you may have different list names depending on where you put your data)  Then push ZOOM 9 to see the scatterplot Example #2.3.2: Scatter Plot Is there any relationship between elevation and high temperature on a given day? The following data are the high temperatures at various cities on a single day and the elevation of the city. Table #2.3.2: Data of Temperature versus Elevation Elevation (in feet) 7000 4000 6000 3000 7000 4500 5000 Temperature (°F) 50 60 48 70 55 55 60 Solution: First identify the individual, variables and type of variables. Individual: Variable 1: Variable 2: Type of variable 1: Type of variable 2: In StatCrunch click on My Data and then click Chapter02DataFile. Follow the directions above using the column called “Elevation (ft)” as the X variable and the column called “Temperature (F)” as the Y variable to get the following: Graph #2.3.6: Scatter Plot of Temperature versus Elevation 53

Chapter 2: Graphical Descriptions of Data Looking at the graph, it appears as elevation increases, the temperature decreases. Section 2.3: Homework 1.) Students in a statistics class took their first test. The data in table #2.3.4 are the scores they earned. Create a stem-and-leaf plot. Table #2.3.4: Data of Test 1 Grades 80 79 89 74 73 67 79 93 70 70 76 88 83 73 81 79 80 85 79 80 79 58 93 94 74 2.) Students in a statistics class took their first test. The data in table #2.3.5 are the scores they earned. Create a stem-and-leaf plot. Compare to the graph in question 1. Table #2.3.5: Data of Test 1 Grades 67 67 76 47 85 70 87 76 80 72 84 98 84 64 65 82 81 81 88 74 87 83 3.) When an anthropologist finds skeletal remains, they need to figure out the height of the person. The height of a person (in cm) and the length of one of their 54

Chapter 2: Graphical Descriptions of Data metacarpal bones (in cm) were recorded for a random sample of 9 living adults and are in table #2.4.6 ("Prediction of height," 2013). Create a scatter plot and state if there is a relationship between the height of a person and the length of their metacarpal. Table #2.3.6: Data of Metacarpal versus Height Length of Metacarpal Height of Person 45 171 51 178 39 157 41 163 48 172 49 183 46 173 43 175 47 173 4.) Table #2.3.7 contains the value of the house and the amount of annual rental income in a year that the house brings in ("Capital and rental," 2013). Create a scatter plot and state if there is a relationship between the value of the house and the annual rental income. Table #2.3.7: Data of House Value versus Rental Value Rental Value Rental Value Rental Value Rental 81000 6656 77000 4576 75000 7280 67500 6864 95000 7904 94000 8736 90000 6240 85000 7072 121000 12064 115000 7904 110000 7072 104000 7904 135000 8320 130000 9776 126000 6240 125000 7904 145000 8320 140000 9568 140000 9152 135000 7488 165000 13312 165000 8528 155000 7488 148000 8320 178000 11856 174000 10400 170000 9568 170000 12688 200000 12272 200000 10608 194000 11232 190000 8320 214000 8528 208000 10400 200000 10400 200000 8320 240000 10192 240000 12064 240000 11648 225000 12480 289000 11648 270000 12896 262000 10192 244500 11232 325000 12480 310000 12480 303000 12272 300000 12480 5.) The World Bank collects information on the life expectancy of a person in each country ("Life expectancy at," 2013) and the fertility rate (number of births per woman) in the country ("Fertility rate," 2013). The data for 24 randomly selected countries for the year 2011 are in table #2.3.8. Create a scatter plot of the data and state if there appears to be a relationship between fertility rate and life expectancy. Table #2.3.8: Data of Life Expectancy versus Fertility Rate 55

Chapter 2: Graphical Descriptions of Data Fertility Rate Life Expectancy Fertility Rate Life Expectancy 1.7 77.2 3.9 72.3 5.8 55.4 1.5 76.0 2.2 69.9 4.2 66.0 2.1 76.4 5.2 55.9 1.8 75.0 6.8 54.4 2.0 78.2 4.7 62.9 2.6 73.0 2.1 78.3 2.8 70.8 2.9 72.1 1.4 82.6 1.4 80.7 2.6 68.9 2.5 74.2 1.5 81.0 1.5 73.3 6.9 54.2 2.4 67.1 6.) The World Bank collected data on the percentage of gross domestic product (GDP) that a country spends on health expenditures ("Health expenditure," 2013) and the percentage of woman receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 is in table #2.3.9. Create a scatter plot of the data and state if there appears to be a relationship between percentage spent on health expenditure and the percentage of woman receiving prenatal care. Table #2.3.9: Data of Prenatal Care versus Health Expenditure Prenatal Care (%) Health Expenditure (% of GDP) 47.9 9.6 54.6 3.7 93.7 5.2 84.7 5.2 100.0 10.0 42.5 4.7 96.4 4.8 77.1 6.0 58.3 5.4 95.4 4.8 78.0 4.1 93.3 6.0 93.3 9.5 93.7 6.8 89.8 6.1 7.) State everything that makes graph #2.3.9 a misleading or poor graph. 56

Chapter 2: Graphical Descriptions of Data Graph #2.3.9: Example of a Poor Graph 8.) State everything that makes graph #2.3.10 a misleading or poor graph (Benen, 2011). Graph #2.3.10: Example of a Poor Graph 57

Chapter 2: Graphical Descriptions of Data 9.) State everything that makes graph #2.3.11 a misleading or poor graph ("United States unemployment," 2013). Graph #2.3.11: Example of a Poor Graph 10.) State everything that makes graph #2.3.12 a misleading or poor graph. Graph #2.3.12: Example of a Poor Graph 58

Chapter 2: Graphical Descriptions of Data Data Sources: B1 assets of financial institutions . (2013, June 27). Retrieved from www.rba.gov.au/statistics/tables/xls/b01hist.xls Benen, S. (2011, September 02). [Web log message]. Retrieved from http://www.washingtonmonthly.com/political-animal/2011_09/gop_leaders_stop_taking_ credit031960.php Capital and rental values of Auckland properties . (2013, September 26). Retrieved from http://www.statsci.org/data/oz/rentcap.html Contraceptive use . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=35 Deaths from firearms . (2013, September 26). Retrieved from http://www.statsci.org/data/oz/firearms.html DeNavas-Walt, C., Proctor, B., & Smith, J. U.S. Department of Commerce, U.S. Census Bureau. (2012). Income, poverty, and health insurance coverage in the United States: 2011 (P60-243). Retrieved from website: www.census.gov/prod/2012pubs/p60-243.pdf Density of people in Africa . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx? ind=30&loc=249,250,251,252,253,254,34227,255,257,258,259,260,261,262,263,264,265 ,266,267,268,269,270,271,272,274,275,276,277,278,279,280,281,282,283,284,285,286,2 87,288,289,290,291,292,294,295,296,297,298,299,300,301,302,304,305,306,307,308 Department of Health and Human Services, ASPE. (2013). Health insurance marketplace premiums for 2014 . Retrieved from website: http://aspe.hhs.gov/health/reports/2013/marketplacepremiums/ib_premiumslandscape.pdf Electricity usage . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=162 Fertility rate . (2013, October 14). Retrieved from http://data.worldbank.org/indicator/SP.DYN.TFRT.IN Fuel oil usage . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=164 Gas usage . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=165 Health expenditure . (2013, October 14). Retrieved from http://data.worldbank.org/indicator/SH.XPD.TOTL.ZS 59

Chapter 2: Graphical Descriptions of Data Hinatov, M. U.S. Consumer Product Safety Commission, Directorate of Epidemiology. (2012). Incidents, deaths, and in-depth investigations associated with non-fire carbon monoxide from engine-driven generators and other engine-driven tools, 1999-2011 . Retrieved from website: http://www.cpsc.gov/PageFiles/129857/cogenerators.pdf Life expectancy at birth . (2013, October 14). Retrieved from http://data.worldbank.org/indicator/SP.DYN.LE00.IN Median income of males . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=137 Median income of males . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/Rankings.aspx?ind=136 Prediction of height from metacarpal bone length . (2013, September 26). Retrieved from http://www.statsci.org/data/general/stature.html Pregnant woman receiving prenatal care . (2013, October 14). Retrieved from http://data.worldbank.org/indicator/SH.STA.ANVC.ZS United States unemployment . (2013, October 14). Retrieved from http://www.tradingeconomics.com/united-states/unemployment-rate Weissmann, J. (2013, March 20). A truly devastating graph on state higher education spending. The Atlantic . Retrieved from http://www.theatlantic.com/business/archive/2013/03/a-truly-devastating-graph-on-state- higher-education-spending/274199/ 60