{"id":399,"date":"2016-10-12T18:02:41","date_gmt":"2016-10-12T18:02:41","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/math4libarts\/?post_type=chapter&#038;p=399"},"modified":"2019-05-30T16:59:03","modified_gmt":"2019-05-30T16:59:03","slug":"presenting-categorical-data-graphically","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/presenting-categorical-data-graphically\/","title":{"raw":"Presenting Categorical Data Graphically","rendered":"Presenting Categorical Data Graphically"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set<\/li>\r\n \t<li>Identify features of ineffective representations of data<\/li>\r\n \t<li>Create a histogram, pie chart, or frequency polygon that represents numerical data<\/li>\r\n \t<li>Create a graph that compares two quantities<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Visualizing Data<\/h2>\r\nCategorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a <strong>frequency table.<\/strong>\r\n<div class=\"textbox\">\r\n<h3>Frequency Table<\/h3>\r\nA frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAn insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Color<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Blue<\/td>\r\n<td>25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Green<\/td>\r\n<td>52<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Red<\/td>\r\n<td>41<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>White<\/td>\r\n<td>36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Black<\/td>\r\n<td>39<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Grey<\/td>\r\n<td>23<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=30765&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"600\"><\/iframe>\r\n\r\n<\/div>\r\nSometimes we need an even more intuitive way of displaying data. This is where charts and graphs come in.\u00a0 There are many, many ways of displaying data graphically, but we will concentrate on one very useful type of graph called a bar graph.\u00a0 In this section we will work with bar graphs that display categorical data; the next section will be devoted to bar graphs that display quantitative data.\r\n<div class=\"textbox\">\r\n<h3>Bar graph<\/h3>\r\nA <strong>bar graph<\/strong> is a graph that displays a bar for each category with the length of each bar indicating the frequency of that category.\r\n\r\n<\/div>\r\nTo construct a bar graph, we need to draw a vertical axis and a horizontal axis.\u00a0 The vertical direction will have a scale and measure the frequency of each category; the horizontal axis has no scale in this instance.\u00a0 The construction of a bar chart is most easily described by use of an example.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nUsing our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units:\r\n\r\n<img class=\"aligncenter wp-image-400\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175120\/vehiclecolor1.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (53), Red (41), White (37), Black (39), Grey (24). \" width=\"350\" height=\"212\" \/>\r\n\r\nNotice that the height of each bar is determined by the frequency of the corresponding color.\u00a0 The horizontal gridlines are a nice touch, but\u00a0not necessary.\u00a0 In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology.\u00a0 Instead of gridlines, we might also list the frequencies at the top of each bar, like this:\r\n\r\n<img class=\"aligncenter wp-image-401\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175208\/vehiclecolor2.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (52), Red (41), White (36), Black (39), Grey (23). \" width=\"350\" height=\"212\" \/>\r\n\r\nThe following video explains the process and value of moving data from a table to a bar graph.\r\n\r\nhttps:\/\/youtu.be\/vwxKf_O3ui0\r\n\r\n<\/div>\r\nIn this case, our chart might benefit from being reordered from largest to smallest frequency values. This arrangement can make it easier to compare similar values in the chart, even without gridlines. When we arrange the categories in decreasing frequency order like this, it is called a <strong>Pareto chart<\/strong>.\r\n<div class=\"textbox\">\r\n<h3>Pareto chart<\/h3>\r\nA <strong>Pareto chart<\/strong> is a bar graph ordered from highest to lowest frequency\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nTransforming our bar graph from earlier into a Pareto chart, we get:\r\n\r\n<img class=\"aligncenter wp-image-402\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175247\/vehiclecolor3.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Green (52), Red (41), Black (39), White (36), Blue (25), Grey (23). \" width=\"350\" height=\"212\" \/>\r\n\r\nThe following video addressed Pareto charts.\r\n\r\nhttps:\/\/youtu.be\/Tsvru8DPxBE\r\n\r\n<hr \/>\r\n\r\nIn a survey[footnote]Gallup Poll. March 5-8, 2009. <a href=\"http:\/\/www.pollingreport.com\/enviro.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/www.pollingreport.com\/enviro.htm<\/a>[\/footnote], adults were asked whether they personally worried about a variety of environmental concerns. The numbers (out of 1012 surveyed) who indicated that they worried \u201ca great deal\u201d about some selected concerns are summarized below.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Environmental Issue<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Pollution of drinking water<\/td>\r\n<td>597<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Contamination of soil and water by toxic waste<\/td>\r\n<td>526<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Air pollution<\/td>\r\n<td>455<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Global warming<\/td>\r\n<td>354<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis data could be shown graphically in a bar graph:\r\n\r\n<img class=\"aligncenter wp-image-403 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175559\/environmentalworries.png\" alt=\"Pareto Bar Graph. Vertical measures Frequency, in units of 100 from 0 - 600. Horizontal measures Environmental Worries. From left, Water Pollution (600), Toxic Waste (~500), Air Pollution (~450), and Global Warming (~350).\" width=\"420\" height=\"184\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nTo show relative sizes, it is common to use a pie chart.\r\n<div class=\"textbox\">\r\n<h3>Pie Chart<\/h3>\r\nA <strong>pie chart<\/strong> is a circle with wedges cut of varying sizes marked out like slices of pie or pizza.\u00a0 The relative sizes of the wedges correspond to the relative frequencies of the categories.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>examples<\/h3>\r\nFor our vehicle color data, a pie chart might look like this:\r\n\r\n<img class=\"aligncenter wp-image-404\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175748\/vehiclepie1.png\" alt=\"Pie Chart titled &quot;Vehicle color involved in total-loss collisions.&quot; Almost one quarter of the pie is green, then red, black, white, blue, and grey is the smallest slice.\" width=\"350\" height=\"176\" \/>\r\n\r\nPie charts can often benefit from including frequencies or relative frequencies (percents) in the chart next to the pie slices. Often having the category names next to the pie slices also makes the chart clearer.\r\n\r\n<img class=\"aligncenter wp-image-405\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175813\/vehiclepie2.png\" alt=\"Pie Chart titled &quot;Vehicle color involved in total-loss collisions.&quot; Almost one quarter of the pie is green (labeled Green, 52), then red (labeled Red, 41), black (labeled Black, 39), white (labeled White, 36), blue (labeled Blue, 25), and grey is the smallest slice (labeled Grey, 23).\" width=\"350\" height=\"176\" \/>\r\n\r\nThis video demonstrates how to <strong>create<\/strong> pie charts like the ones above.\r\n\r\nhttps:\/\/youtu.be\/__1f8dKh6yo\r\n\r\n<hr \/>\r\n\r\nThe pie chart below\u00a0shows the percentage of voters supporting each candidate running for a local senate seat.\r\n\r\nIf there are 20,000 voters in the district, the pie chart shows that about 11% of those, about 2,200 voters, support Reeves.\r\n\r\n<img class=\"aligncenter wp-image-406\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175832\/voter1.png\" alt=\"Pie Chart labeled Voter preferences. Almost half the left side is black (labeled Elison, 46%), Most of the right is green (labeled Douglas, 43%), and a small portion near the bottom is red (labeled Reeves 11%).\" width=\"349\" height=\"234\" \/>\r\n\r\nThe following video addresses how to <strong>read<\/strong> a pie chart like the one above.\r\n\r\nhttps:\/\/youtu.be\/mwa8vQnGr3I\r\n\r\n<\/div>\r\nPie charts look nice, but are harder to draw by hand than bar charts since to draw them accurately we would need to compute the angle each wedge cuts out of the circle, then measure the angle with a protractor. Computers are much better suited to drawing pie charts. Common software programs like Microsoft Word or Excel, OpenOffice.org Write or Calc, or Google Drive\u00a0are able to create bar graphs, pie charts, and other graph types. There are also numerous online tools that can create graphs.[footnote]For example: <a href=\"http:\/\/nces.ed.gov\/nceskids\/createAgraph\/\" target=\"_blank\" rel=\"noopener\">http:\/\/nces.ed.gov\/nceskids\/createAgraph\/<\/a> or <a href=\"http:\/\/docs.google.com\" target=\"_blank\" rel=\"noopener\">http:\/\/docs.google.com<\/a>[\/footnote]\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nCreate a bar graph and a pie chart to illustrate the grades on a history exam below.\r\n\r\nA: 12 students, B: 19 students, C: 14 students, D: 4 students, F: 5 students\r\n\r\n<iframe id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1059&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"400\"><\/iframe>\r\n\r\n<\/div>\r\nDon\u2019t get fancy with graphs! People sometimes add features to graphs that don\u2019t help to convey their information. For example, 3-dimensional bar charts like the one shown below are usually not as effective as their two-dimensional counterparts.<img class=\"aligncenter wp-image-407\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175910\/carcolorbar.png\" alt=\"3D Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (52), Red (41), White (36), Grey (23), Black (39). The tilted angle of the display makes it difficult to line up the top of the bar with the frequency numbers.\" width=\"350\" height=\"211\" \/>\r\n\r\nHere is another way that fanciness can lead to trouble. Instead of plain bars, it is tempting to substitute meaningful images. This type of graph is called a <strong>pictogram<\/strong>.\r\n<div class=\"textbox\">\r\n<h3>Pictogram<\/h3>\r\nA <strong>pictogram<\/strong> is a statistical graphic in which the size of the picture is intended to represent the frequencies or size of the values being represented.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n<img class=\"alignright wp-image-408\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175957\/moneybag.png\" alt=\"Two drawings of money bags, one on the left substantially larger than the one on the right. Left is labeled Manager Salaries, right is labeled Worker Salaries.\" width=\"200\" height=\"216\" \/>A labor union might produce the graph to the right to show the difference between the average manager salary and the average worker salary.\r\n\r\nLooking at the picture, it would be reasonable to guess that the manager salaries is 4 times as large as the worker salaries \u2013 the area of the bag looks about 4 times as large. However, the manager salaries are in fact only twice as large as worker salaries, which were reflected in the picture by making the manager bag twice as tall.\r\n\r\nThis video reviews the two examples of ineffective\u00a0data representation in more detail.\r\n\r\nhttps:\/\/youtu.be\/bFwTZNGNLKs\r\n\r\n<\/div>\r\nAnother distortion in bar charts results from setting the baseline to a value other than zero. The baseline is the bottom of the vertical axis, representing the least number of cases that could have occurred in a category. Normally, this number should be zero.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nCompare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008[footnote]CNN\/Opinion Research Corporation Poll. Dec 19-21, 2008, from <a href=\"http:\/\/www.pollingreport.com\/civil.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/www.pollingreport.com\/civil.htm<\/a>[\/footnote].\u00a0The difference in the vertical scale on the first graph suggests a different story than the true differences in percentages; the second graph makes it look like twice as many people oppose marriage rights as support it.\r\n\r\n<img class=\"wp-image-409 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180109\/supportopposebar.png\" alt=\"Bar graph. Vertical measures Frequency (%), in increments of 10 from 0-100. Horizontal measures Do you support or oppose a same-sex marriage? Support (~40%), Oppose (~50%).\" width=\"350\" height=\"292\" \/><img class=\"wp-image-410 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180134\/supportoppose2.png\" alt=\"Bar graph. Vertical measures Frequency (%), in increments of 5 from 40-60. Horizontal measures Do you support or oppose a same-sex marriage? Support (~43%), Oppose (~55%).\" width=\"350\" height=\"292\" \/>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nA poll was taken asking people if they agreed with the positions of the 4 candidates for a county office. Does the pie chart present a good representation of this data? Explain.<img class=\"size-full wp-image-411 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180208\/nguyenmckee.png\" alt=\"nguyenmckee\" width=\"212\" height=\"125\" \/>\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set<\/li>\n<li>Identify features of ineffective representations of data<\/li>\n<li>Create a histogram, pie chart, or frequency polygon that represents numerical data<\/li>\n<li>Create a graph that compares two quantities<\/li>\n<\/ul>\n<\/div>\n<h2>Visualizing Data<\/h2>\n<p>Categorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a <strong>frequency table.<\/strong><\/p>\n<div class=\"textbox\">\n<h3>Frequency Table<\/h3>\n<p>A frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>An insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Color<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Blue<\/td>\n<td>25<\/td>\n<\/tr>\n<tr>\n<td>Green<\/td>\n<td>52<\/td>\n<\/tr>\n<tr>\n<td>Red<\/td>\n<td>41<\/td>\n<\/tr>\n<tr>\n<td>White<\/td>\n<td>36<\/td>\n<\/tr>\n<tr>\n<td>Black<\/td>\n<td>39<\/td>\n<\/tr>\n<tr>\n<td>Grey<\/td>\n<td>23<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=30765&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"600\"><\/iframe><\/p>\n<\/div>\n<p>Sometimes we need an even more intuitive way of displaying data. This is where charts and graphs come in.\u00a0 There are many, many ways of displaying data graphically, but we will concentrate on one very useful type of graph called a bar graph.\u00a0 In this section we will work with bar graphs that display categorical data; the next section will be devoted to bar graphs that display quantitative data.<\/p>\n<div class=\"textbox\">\n<h3>Bar graph<\/h3>\n<p>A <strong>bar graph<\/strong> is a graph that displays a bar for each category with the length of each bar indicating the frequency of that category.<\/p>\n<\/div>\n<p>To construct a bar graph, we need to draw a vertical axis and a horizontal axis.\u00a0 The vertical direction will have a scale and measure the frequency of each category; the horizontal axis has no scale in this instance.\u00a0 The construction of a bar chart is most easily described by use of an example.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Using our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-400\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175120\/vehiclecolor1.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (53), Red (41), White (37), Black (39), Grey (24).\" width=\"350\" height=\"212\" \/><\/p>\n<p>Notice that the height of each bar is determined by the frequency of the corresponding color.\u00a0 The horizontal gridlines are a nice touch, but\u00a0not necessary.\u00a0 In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology.\u00a0 Instead of gridlines, we might also list the frequencies at the top of each bar, like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-401\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175208\/vehiclecolor2.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (52), Red (41), White (36), Black (39), Grey (23).\" width=\"350\" height=\"212\" \/><\/p>\n<p>The following video explains the process and value of moving data from a table to a bar graph.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Bar graphs for categorical data\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vwxKf_O3ui0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>In this case, our chart might benefit from being reordered from largest to smallest frequency values. This arrangement can make it easier to compare similar values in the chart, even without gridlines. When we arrange the categories in decreasing frequency order like this, it is called a <strong>Pareto chart<\/strong>.<\/p>\n<div class=\"textbox\">\n<h3>Pareto chart<\/h3>\n<p>A <strong>Pareto chart<\/strong> is a bar graph ordered from highest to lowest frequency<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>Transforming our bar graph from earlier into a Pareto chart, we get:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-402\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175247\/vehiclecolor3.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Green (52), Red (41), Black (39), White (36), Blue (25), Grey (23).\" width=\"350\" height=\"212\" \/><\/p>\n<p>The following video addressed Pareto charts.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Pareto Chart\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Tsvru8DPxBE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<hr \/>\n<p>In a survey<a class=\"footnote\" title=\"Gallup Poll. March 5-8, 2009. http:\/\/www.pollingreport.com\/enviro.htm\" id=\"return-footnote-399-1\" href=\"#footnote-399-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>, adults were asked whether they personally worried about a variety of environmental concerns. The numbers (out of 1012 surveyed) who indicated that they worried \u201ca great deal\u201d about some selected concerns are summarized below.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Environmental Issue<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Pollution of drinking water<\/td>\n<td>597<\/td>\n<\/tr>\n<tr>\n<td>Contamination of soil and water by toxic waste<\/td>\n<td>526<\/td>\n<\/tr>\n<tr>\n<td>Air pollution<\/td>\n<td>455<\/td>\n<\/tr>\n<tr>\n<td>Global warming<\/td>\n<td>354<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This data could be shown graphically in a bar graph:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-403 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175559\/environmentalworries.png\" alt=\"Pareto Bar Graph. Vertical measures Frequency, in units of 100 from 0 - 600. Horizontal measures Environmental Worries. From left, Water Pollution (600), Toxic Waste (~500), Air Pollution (~450), and Global Warming (~350).\" width=\"420\" height=\"184\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>To show relative sizes, it is common to use a pie chart.<\/p>\n<div class=\"textbox\">\n<h3>Pie Chart<\/h3>\n<p>A <strong>pie chart<\/strong> is a circle with wedges cut of varying sizes marked out like slices of pie or pizza.\u00a0 The relative sizes of the wedges correspond to the relative frequencies of the categories.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>examples<\/h3>\n<p>For our vehicle color data, a pie chart might look like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-404\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175748\/vehiclepie1.png\" alt=\"Pie Chart titled &quot;Vehicle color involved in total-loss collisions.&quot; Almost one quarter of the pie is green, then red, black, white, blue, and grey is the smallest slice.\" width=\"350\" height=\"176\" \/><\/p>\n<p>Pie charts can often benefit from including frequencies or relative frequencies (percents) in the chart next to the pie slices. Often having the category names next to the pie slices also makes the chart clearer.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-405\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175813\/vehiclepie2.png\" alt=\"Pie Chart titled &quot;Vehicle color involved in total-loss collisions.&quot; Almost one quarter of the pie is green (labeled Green, 52), then red (labeled Red, 41), black (labeled Black, 39), white (labeled White, 36), blue (labeled Blue, 25), and grey is the smallest slice (labeled Grey, 23).\" width=\"350\" height=\"176\" \/><\/p>\n<p>This video demonstrates how to <strong>create<\/strong> pie charts like the ones above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Creating a pie chart\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/__1f8dKh6yo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<hr \/>\n<p>The pie chart below\u00a0shows the percentage of voters supporting each candidate running for a local senate seat.<\/p>\n<p>If there are 20,000 voters in the district, the pie chart shows that about 11% of those, about 2,200 voters, support Reeves.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-406\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175832\/voter1.png\" alt=\"Pie Chart labeled Voter preferences. Almost half the left side is black (labeled Elison, 46%), Most of the right is green (labeled Douglas, 43%), and a small portion near the bottom is red (labeled Reeves 11%).\" width=\"349\" height=\"234\" \/><\/p>\n<p>The following video addresses how to <strong>read<\/strong> a pie chart like the one above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Reading a pie chart\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/mwa8vQnGr3I?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Pie charts look nice, but are harder to draw by hand than bar charts since to draw them accurately we would need to compute the angle each wedge cuts out of the circle, then measure the angle with a protractor. Computers are much better suited to drawing pie charts. Common software programs like Microsoft Word or Excel, OpenOffice.org Write or Calc, or Google Drive\u00a0are able to create bar graphs, pie charts, and other graph types. There are also numerous online tools that can create graphs.<a class=\"footnote\" title=\"For example: http:\/\/nces.ed.gov\/nceskids\/createAgraph\/ or http:\/\/docs.google.com\" id=\"return-footnote-399-2\" href=\"#footnote-399-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Create a bar graph and a pie chart to illustrate the grades on a history exam below.<\/p>\n<p>A: 12 students, B: 19 students, C: 14 students, D: 4 students, F: 5 students<\/p>\n<p><iframe loading=\"lazy\" id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=1059&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>Don\u2019t get fancy with graphs! People sometimes add features to graphs that don\u2019t help to convey their information. For example, 3-dimensional bar charts like the one shown below are usually not as effective as their two-dimensional counterparts.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-407\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175910\/carcolorbar.png\" alt=\"3D Bar graph. Vertical measures Frequency, in increments of 5 from 0 to 55. Horizontal measures Vehicle color involved in a total-loss collision, showing from left Blue (25), Green (52), Red (41), White (36), Grey (23), Black (39). The tilted angle of the display makes it difficult to line up the top of the bar with the frequency numbers.\" width=\"350\" height=\"211\" \/><\/p>\n<p>Here is another way that fanciness can lead to trouble. Instead of plain bars, it is tempting to substitute meaningful images. This type of graph is called a <strong>pictogram<\/strong>.<\/p>\n<div class=\"textbox\">\n<h3>Pictogram<\/h3>\n<p>A <strong>pictogram<\/strong> is a statistical graphic in which the size of the picture is intended to represent the frequencies or size of the values being represented.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-408\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12175957\/moneybag.png\" alt=\"Two drawings of money bags, one on the left substantially larger than the one on the right. Left is labeled Manager Salaries, right is labeled Worker Salaries.\" width=\"200\" height=\"216\" \/>A labor union might produce the graph to the right to show the difference between the average manager salary and the average worker salary.<\/p>\n<p>Looking at the picture, it would be reasonable to guess that the manager salaries is 4 times as large as the worker salaries \u2013 the area of the bag looks about 4 times as large. However, the manager salaries are in fact only twice as large as worker salaries, which were reflected in the picture by making the manager bag twice as tall.<\/p>\n<p>This video reviews the two examples of ineffective\u00a0data representation in more detail.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Bad graphical represenations of data\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bFwTZNGNLKs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Another distortion in bar charts results from setting the baseline to a value other than zero. The baseline is the bottom of the vertical axis, representing the least number of cases that could have occurred in a category. Normally, this number should be zero.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Compare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008<a class=\"footnote\" title=\"CNN\/Opinion Research Corporation Poll. Dec 19-21, 2008, from http:\/\/www.pollingreport.com\/civil.htm\" id=\"return-footnote-399-3\" href=\"#footnote-399-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a>.\u00a0The difference in the vertical scale on the first graph suggests a different story than the true differences in percentages; the second graph makes it look like twice as many people oppose marriage rights as support it.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-409 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180109\/supportopposebar.png\" alt=\"Bar graph. Vertical measures Frequency (%), in increments of 10 from 0-100. Horizontal measures Do you support or oppose a same-sex marriage? Support (~40%), Oppose (~50%).\" width=\"350\" height=\"292\" \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-410 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180134\/supportoppose2.png\" alt=\"Bar graph. Vertical measures Frequency (%), in increments of 5 from 40-60. Horizontal measures Do you support or oppose a same-sex marriage? Support (~43%), Oppose (~55%).\" width=\"350\" height=\"292\" \/><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>A poll was taken asking people if they agreed with the positions of the 4 candidates for a county office. Does the pie chart present a good representation of this data? Explain.<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-411 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180208\/nguyenmckee.png\" alt=\"nguyenmckee\" width=\"212\" height=\"125\" \/><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-399\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Presenting Categorical Data Graphically. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Math in Society. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Bar graphs for categorical data. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/vwxKf_O3ui0\">https:\/\/youtu.be\/vwxKf_O3ui0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Pareto Chart. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Tsvru8DPxBE\">https:\/\/youtu.be\/Tsvru8DPxBE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Creating a pie chart. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/__1f8dKh6yo\">https:\/\/youtu.be\/__1f8dKh6yo<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Reading a pie chart. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/mwa8vQnGr3I\">https:\/\/youtu.be\/mwa8vQnGr3I<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Bad graphical represenations of data. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/bFwTZNGNLKs\">https:\/\/youtu.be\/bFwTZNGNLKs<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-399-1\">Gallup Poll. March 5-8, 2009. <a href=\"http:\/\/www.pollingreport.com\/enviro.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/www.pollingreport.com\/enviro.htm<\/a> <a href=\"#return-footnote-399-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-399-2\">For example: <a href=\"http:\/\/nces.ed.gov\/nceskids\/createAgraph\/\" target=\"_blank\" rel=\"noopener\">http:\/\/nces.ed.gov\/nceskids\/createAgraph\/<\/a> or <a href=\"http:\/\/docs.google.com\" target=\"_blank\" rel=\"noopener\">http:\/\/docs.google.com<\/a> <a href=\"#return-footnote-399-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-399-3\">CNN\/Opinion Research Corporation Poll. Dec 19-21, 2008, from <a href=\"http:\/\/www.pollingreport.com\/civil.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/www.pollingreport.com\/civil.htm<\/a> <a href=\"#return-footnote-399-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":20,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Presenting Categorical Data Graphically\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"Math in Society\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Bar graphs for categorical data\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/vwxKf_O3ui0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Pareto Chart\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Tsvru8DPxBE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Creating a pie chart\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/__1f8dKh6yo\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Reading a pie chart\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/mwa8vQnGr3I\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Bad graphical represenations of data\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/bFwTZNGNLKs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"81946ddb-7dbe-40d1-878c-220a6a47b5ea","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-399","chapter","type-chapter","status-publish","hentry"],"part":398,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/20"}],"version-history":[{"count":16,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/399\/revisions"}],"predecessor-version":[{"id":3030,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/399\/revisions\/3030"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/398"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}