{"id":389,"date":"2022-06-17T16:48:57","date_gmt":"2022-06-17T16:48:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&#038;p=389"},"modified":"2022-06-17T16:48:57","modified_gmt":"2022-06-17T16:48:57","slug":"displaying-categorical-data-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/displaying-categorical-data-background-youll-need-2\/","title":{"raw":"Displaying Categorical Data: Background You'll Need 2","rendered":"Displaying Categorical Data: Background You&#8217;ll Need 2"},"content":{"raw":"<h3 id=\"BarGraph\">Bar graphs<\/h3>\r\nBar graphs are visual displays of data in which the frequency of each category listed across the horizontal axis is indicated by the height of its corresponding rectangular bar (or the length if the graph is displayed horizontally). Bar graphs can be displayed vertically, as the ones you'll see here, or horizontally. See the interactive example below for a demonstration of how to read a bar graph.\r\n<div class=\"textbox exercises\">\r\n<h3>Interactive example<\/h3>\r\nThe graph you see here is a portion of a larger graph that you'll see following this demonstration. The full graph will display data about internationally occurring shark attacks. This portion shows just the attacks in the United States. The states are listed, one by one across the horizontal axis. Each bar rises to a number along the vertical axis representing the number of shark attacks recorded in that state.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-1068\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/14163508\/3A_BarGraph_Example.png\" alt=\"A bar graph Titled Shark Attacks in the U.S. show the states Florida, Hawaii, South Caroline, California, and North Carolina along the horizontal axis. The vertical axis is labeled Count. The bar above Florida rises to just above 200. The bar above Hawaii rises to about 50. The bars above South Carolina and California rise to approximately the same height, at about 35 and the bar above North Carolina rises the least, to about 25.\" width=\"653\" height=\"350\" \/>\r\n\r\nUse this chart (rather than the frequency table you saw earlier) to answer the following questions.\r\n<ol>\r\n \t<li>According to the bar graph, about how many shark attacks occurred in Florida?<\/li>\r\n \t<li>What two states appear to have recorded about the same number of attacks?<\/li>\r\n \t<li>About how many attacks does the bar graph indicate occurred in Hawaii?<\/li>\r\n \t<li>About how many attacks occurred in North Carolina?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"718230\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"718230\"]\r\n<ol>\r\n \t<li>It looks like about 200 attacks were in Florida.<\/li>\r\n \t<li>South Carolina and California appear to have recorded about 35 each.<\/li>\r\n \t<li>Hawaii had about 50 shark attacks.<\/li>\r\n \t<li>North Carolina had about 25 attacks.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div style=\"text-align: left;\">\r\n\r\nNow it's your turn to try reading a bar graph. The image below is\u00a0<span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">a bar graph (also known as a bar chart) of [latex]689[\/latex] shark attacks across the globe.[footnote]Sharks (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-db346c01b1b3\/downloads\/sharks.csv?ver=1622756678385[\/footnote] Note that each country or state is listed along the horizontal axis. The height of each bar provides a visual representation of the number (count) of shark attacks that occurred in each country. We cannot read the exact frequency of each bar from a bar graph. Rather, the display helps us to visualize the frequencies relative to one another.<\/span>\r\n\r\n<img class=\"aligncenter wp-image-1067 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233624\/3A-Bar-Chart.png\" alt=\"A bar graph of shark attacks across various regions. The vertical axis is labeled &quot;Count&quot; and numbered in increments of 50 up to 200 and the horizontal is labeled &quot;Region.&quot; The bar for Florida reaches the top of the chart. The bar for Hawaii goes to the line at 50. The bar for South Carolina goes approximately two thirds of the way to the line at 50. The bar for California goes approximately two thirds of the way to the line at 50. The bar for North Carolina goes approximately halfway to the line at 50. The bar for Australia goes to approximately halfway between the line at 100 and the line at 150. The bar for South Africa goes almost to the line at 50. The bar for Reunion Island goes approximately one third of the way to the line at 50. The bar for Brazil goes approximately one third of the way to the line at 50. The bar for the Bahamas goes approximately one fifth of the way to the line at 50. The bar for other regions goes to approximately three quarters of the way between the line at 100 and the line at 150. \" width=\"1024\" height=\"293\" \/>\r\n\r\nUse the chart to answer the questions below.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240678[\/ohm_question]\r\n\r\n[reveal-answer q=\"528508\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"528508\"]The height of the bars in the graph indicate the frequency (count) in each category. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240672[\/ohm_question]\r\n\r\n[reveal-answer q=\"797453\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"797453\"]See the Count displayed on the vertical axis. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240673[\/ohm_question]\r\n\r\n[reveal-answer q=\"915074\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"915074\"]To estimate a percent, first estimate the ratio of attacks in Australia to the total, then convert the ratio to a percent.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"PieChart\">Pie Charts<\/h3>\r\nPie charts display data in a round graph, split into \"pie pieces,\" each representing a relative frequency. A key is provided to identify the categories associated with each relative frequency. Pie charts are useful for visually comparing relative frequencies.\r\n<div class=\"textbox exercises\">\r\n<h3>Interactive example<\/h3>\r\nLet's say we were interested in comparing the percentage of shark attacks occurring in the United States and Australia versus the rest of the globe. We could create pie chart like the one below. This chart takes [latex]689[\/latex] international shark attacks and divides them into three categories: attacks occurring in the United States, in Australia, and all other locations.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter wp-image-1069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233917\/3A-Pie-Chart.png\" alt=\"A pie chart of International Shark Attacks showing 56.2% in the United States, 18.1% in Australia, and 25.7% in other countries\" width=\"555\" height=\"357\" \/>\r\n\r\nUse this pie chart to answer the following questions.\r\n<ol>\r\n \t<li>What percent of attacks happened in Australia?<\/li>\r\n \t<li>Approximately how many of the total 689 attacks happened in Australia?<\/li>\r\n<\/ol>\r\nIf needed, see the recall box below to refresh how to determine what number a certain percent represents in a given total.\r\n\r\n[reveal-answer q=\"645182\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"645182\"]\r\n<ol>\r\n \t<li>[latex]18.1\\%[\/latex] of all attacks happened in Australia, which we can read directly from the chart.<\/li>\r\n \t<li>About [latex]125[\/latex] attacks happened in Australia.\r\n<ul>\r\n \t<li><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">This is same as asking the question\u00a0<em>what is<\/em> [latex]\\textit{18.1%}[\/latex] <em>of<\/em> [latex]\\textit{689}[\/latex]?\u00a0<\/span><\/li>\r\n \t<li>[latex]0.181\\times689=124.709[\/latex], which rounds up to [latex]125[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<p style=\"padding-left: 30px;\"><em>Relative frequencies written as percentages are often approximations due to having rounded them for the display. For this reason, the percentages don't always add up to exactly [latex]100[\/latex]%, but they will be close.<\/em><\/p>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nWhen working with percentages, it is often helpful to convert them to counts.\r\n\r\nCore skill:\r\n[reveal-answer q=\"66574\"]Given a total, convert a percent of the total into a number.[\/reveal-answer]\r\n[hidden-answer a=\"66574\"]\r\n\r\nLet's use the percentage of shark attacks in North Carolina from the table above as an example.\r\n\r\nWe know that [latex]23[\/latex] of the U.S. attacks happened in North Carolina, which represented [latex]5.94[\/latex]% of the total [latex]387[\/latex] attacks. Let's work backwards to obtain the number [latex]23[\/latex] given the percent and total.\r\n\r\nEx. Given that [latex]5.94[\/latex]% of [latex]387[\/latex] attacks occurred in North Carolina, how many attacks is that?\r\n\r\nFirst, we'll need to translate [latex]5.94[\/latex]% into a number. To do so, drop the percent symbol and divide by [latex]100[\/latex] (move the decimal two places to the left).\u00a0[latex]5.94[\/latex]% becomes [latex]0.0594[\/latex].\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}=0.0594[\/latex]<\/p>\r\nThen, multiply the total by [latex]0.0594[\/latex] ([latex]5.94[\/latex]%\u00a0<em>of<\/em> [latex]387[\/latex]; commonly in math the word\u00a0<em>of<\/em> translates to\u00a0<em>multiply<\/em>)\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}\\times387=0.0594 \\times 387 = 22.9878 \\approx 23[\/latex].<\/p>\r\n<strong>[latex]5.94[\/latex]% of the total represents about [latex]23[\/latex] shark attacks.<\/strong>\r\n\r\nWhy did we obtain [latex]22.9878[\/latex] as our answer rather than [latex]23[\/latex]? Recall that we had rounded the answer to [latex]\\frac{23}{387}[\/latex] to obtain the proportion [latex]0.0594[\/latex] and percent [latex]5.94[\/latex]%.\u00a0We've reversed the process we initially applied to write [latex]\\frac{23}{387}[\/latex] as a percent!\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn. Here is the pie chart from the interactive example above showing the relative frequencies of all [latex]689[\/latex] international shark attacks that occurred in the U.S., Australia, and all other locations.\r\n\r\n<img class=\"aligncenter wp-image-1069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233917\/3A-Pie-Chart.png\" alt=\"A pie chart of International Shark Attacks showing 56.2% in the United States, 18.1% in Australia, and 25.7% in other countries\" width=\"555\" height=\"357\" \/>\r\n\r\nUse the pie chart above to answer the following two questions.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240674[\/ohm_question]\r\n\r\n[reveal-answer q=\"667791\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"667791\"]Use the key to discover which pie slice represents the percentage of attacks in the U.S.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]240675[\/ohm_question]\r\n\r\n[reveal-answer q=\"998027\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"998027\"]See the recall box for help converting a percent to a count.[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's try one more.\u00a0The following is a pie chart of [latex]387[\/latex] shark attacks in the United States. Use the information from the table to determine how many shark attacks in each of the two categories shown.\r\n\r\n<img class=\"aligncenter wp-image-1070\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11234032\/3A-Pie-Chart-2.png\" alt=\"A pie chart of shark attacks in the United States showing 52.5% in Florida and 47.5% in all other states\" width=\"589\" height=\"378\" \/>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]240676[\/ohm_question]\r\n\r\n[reveal-answer q=\"216877\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"216877\"]There were 387 total attacks (given in the text above). See the pie chart key to obtain the necessary percentage. Round to the nearest whole number (up or down).[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]240677[\/ohm_question]\r\n\r\n[reveal-answer q=\"17985\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"17985\"]There were 387 total attacks (given in the text above). See the pie chart key to obtain the necessary percentage. Round to the nearest whole number (up or down).[\/hidden-answer]\r\n\r\n<\/div>\r\nYou've seen how to read information presented in frequency tables, bar charts, and pie charts and you've learned to calculate relative frequencies. You've also seen how to interpret the information displayed, and that sometimes it is helpful to convert numbers between ratios, proportions, and percentages in doing so. If you feel comfortable with these skills, then it's time to move on to the next section.","rendered":"<h3 id=\"BarGraph\">Bar graphs<\/h3>\n<p>Bar graphs are visual displays of data in which the frequency of each category listed across the horizontal axis is indicated by the height of its corresponding rectangular bar (or the length if the graph is displayed horizontally). Bar graphs can be displayed vertically, as the ones you&#8217;ll see here, or horizontally. See the interactive example below for a demonstration of how to read a bar graph.<\/p>\n<div class=\"textbox exercises\">\n<h3>Interactive example<\/h3>\n<p>The graph you see here is a portion of a larger graph that you&#8217;ll see following this demonstration. The full graph will display data about internationally occurring shark attacks. This portion shows just the attacks in the United States. The states are listed, one by one across the horizontal axis. Each bar rises to a number along the vertical axis representing the number of shark attacks recorded in that state.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1068\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/14163508\/3A_BarGraph_Example.png\" alt=\"A bar graph Titled Shark Attacks in the U.S. show the states Florida, Hawaii, South Caroline, California, and North Carolina along the horizontal axis. The vertical axis is labeled Count. The bar above Florida rises to just above 200. The bar above Hawaii rises to about 50. The bars above South Carolina and California rise to approximately the same height, at about 35 and the bar above North Carolina rises the least, to about 25.\" width=\"653\" height=\"350\" \/><\/p>\n<p>Use this chart (rather than the frequency table you saw earlier) to answer the following questions.<\/p>\n<ol>\n<li>According to the bar graph, about how many shark attacks occurred in Florida?<\/li>\n<li>What two states appear to have recorded about the same number of attacks?<\/li>\n<li>About how many attacks does the bar graph indicate occurred in Hawaii?<\/li>\n<li>About how many attacks occurred in North Carolina?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q718230\">Show Answer<\/span><\/p>\n<div id=\"q718230\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>It looks like about 200 attacks were in Florida.<\/li>\n<li>South Carolina and California appear to have recorded about 35 each.<\/li>\n<li>Hawaii had about 50 shark attacks.<\/li>\n<li>North Carolina had about 25 attacks.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"text-align: left;\">\n<p>Now it&#8217;s your turn to try reading a bar graph. The image below is\u00a0<span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">a bar graph (also known as a bar chart) of [latex]689[\/latex] shark attacks across the globe.<a class=\"footnote\" title=\"Sharks (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-db346c01b1b3\/downloads\/sharks.csv?ver=1622756678385\" id=\"return-footnote-389-1\" href=\"#footnote-389-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Note that each country or state is listed along the horizontal axis. The height of each bar provides a visual representation of the number (count) of shark attacks that occurred in each country. We cannot read the exact frequency of each bar from a bar graph. Rather, the display helps us to visualize the frequencies relative to one another.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1067 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233624\/3A-Bar-Chart.png\" alt=\"A bar graph of shark attacks across various regions. The vertical axis is labeled &quot;Count&quot; and numbered in increments of 50 up to 200 and the horizontal is labeled &quot;Region.&quot; The bar for Florida reaches the top of the chart. The bar for Hawaii goes to the line at 50. The bar for South Carolina goes approximately two thirds of the way to the line at 50. The bar for California goes approximately two thirds of the way to the line at 50. The bar for North Carolina goes approximately halfway to the line at 50. The bar for Australia goes to approximately halfway between the line at 100 and the line at 150. The bar for South Africa goes almost to the line at 50. The bar for Reunion Island goes approximately one third of the way to the line at 50. The bar for Brazil goes approximately one third of the way to the line at 50. The bar for the Bahamas goes approximately one fifth of the way to the line at 50. The bar for other regions goes to approximately three quarters of the way between the line at 100 and the line at 150.\" width=\"1024\" height=\"293\" \/><\/p>\n<p>Use the chart to answer the questions below.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240678\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240678&theme=oea&iframe_resize_id=ohm240678\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q528508\">Hint<\/span><\/p>\n<div id=\"q528508\" class=\"hidden-answer\" style=\"display: none\">The height of the bars in the graph indicate the frequency (count) in each category. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240672\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240672&theme=oea&iframe_resize_id=ohm240672\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q797453\">Hint<\/span><\/p>\n<div id=\"q797453\" class=\"hidden-answer\" style=\"display: none\">See the Count displayed on the vertical axis. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240673\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240673&theme=oea&iframe_resize_id=ohm240673\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q915074\">Hint<\/span><\/p>\n<div id=\"q915074\" class=\"hidden-answer\" style=\"display: none\">To estimate a percent, first estimate the ratio of attacks in Australia to the total, then convert the ratio to a percent.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"PieChart\">Pie Charts<\/h3>\n<p>Pie charts display data in a round graph, split into &#8220;pie pieces,&#8221; each representing a relative frequency. A key is provided to identify the categories associated with each relative frequency. Pie charts are useful for visually comparing relative frequencies.<\/p>\n<div class=\"textbox exercises\">\n<h3>Interactive example<\/h3>\n<p>Let&#8217;s say we were interested in comparing the percentage of shark attacks occurring in the United States and Australia versus the rest of the globe. We could create pie chart like the one below. This chart takes [latex]689[\/latex] international shark attacks and divides them into three categories: attacks occurring in the United States, in Australia, and all other locations.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233917\/3A-Pie-Chart.png\" alt=\"A pie chart of International Shark Attacks showing 56.2% in the United States, 18.1% in Australia, and 25.7% in other countries\" width=\"555\" height=\"357\" \/><\/p>\n<p>Use this pie chart to answer the following questions.<\/p>\n<ol>\n<li>What percent of attacks happened in Australia?<\/li>\n<li>Approximately how many of the total 689 attacks happened in Australia?<\/li>\n<\/ol>\n<p>If needed, see the recall box below to refresh how to determine what number a certain percent represents in a given total.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q645182\">Show Answer<\/span><\/p>\n<div id=\"q645182\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]18.1\\%[\/latex] of all attacks happened in Australia, which we can read directly from the chart.<\/li>\n<li>About [latex]125[\/latex] attacks happened in Australia.\n<ul>\n<li><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">This is same as asking the question\u00a0<em>what is<\/em> [latex]\\textit{18.1%}[\/latex] <em>of<\/em> [latex]\\textit{689}[\/latex]?\u00a0<\/span><\/li>\n<li>[latex]0.181\\times689=124.709[\/latex], which rounds up to [latex]125[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p style=\"padding-left: 30px;\"><em>Relative frequencies written as percentages are often approximations due to having rounded them for the display. For this reason, the percentages don&#8217;t always add up to exactly [latex]100[\/latex]%, but they will be close.<\/em><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>When working with percentages, it is often helpful to convert them to counts.<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q66574\">Given a total, convert a percent of the total into a number.<\/span><\/p>\n<div id=\"q66574\" class=\"hidden-answer\" style=\"display: none\">\n<p>Let&#8217;s use the percentage of shark attacks in North Carolina from the table above as an example.<\/p>\n<p>We know that [latex]23[\/latex] of the U.S. attacks happened in North Carolina, which represented [latex]5.94[\/latex]% of the total [latex]387[\/latex] attacks. Let&#8217;s work backwards to obtain the number [latex]23[\/latex] given the percent and total.<\/p>\n<p>Ex. Given that [latex]5.94[\/latex]% of [latex]387[\/latex] attacks occurred in North Carolina, how many attacks is that?<\/p>\n<p>First, we&#8217;ll need to translate [latex]5.94[\/latex]% into a number. To do so, drop the percent symbol and divide by [latex]100[\/latex] (move the decimal two places to the left).\u00a0[latex]5.94[\/latex]% becomes [latex]0.0594[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}=0.0594[\/latex]<\/p>\n<p>Then, multiply the total by [latex]0.0594[\/latex] ([latex]5.94[\/latex]%\u00a0<em>of<\/em> [latex]387[\/latex]; commonly in math the word\u00a0<em>of<\/em> translates to\u00a0<em>multiply<\/em>)<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}\\times387=0.0594 \\times 387 = 22.9878 \\approx 23[\/latex].<\/p>\n<p><strong>[latex]5.94[\/latex]% of the total represents about [latex]23[\/latex] shark attacks.<\/strong><\/p>\n<p>Why did we obtain [latex]22.9878[\/latex] as our answer rather than [latex]23[\/latex]? Recall that we had rounded the answer to [latex]\\frac{23}{387}[\/latex] to obtain the proportion [latex]0.0594[\/latex] and percent [latex]5.94[\/latex]%.\u00a0We&#8217;ve reversed the process we initially applied to write [latex]\\frac{23}{387}[\/latex] as a percent!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now it&#8217;s your turn. Here is the pie chart from the interactive example above showing the relative frequencies of all [latex]689[\/latex] international shark attacks that occurred in the U.S., Australia, and all other locations.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1069\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11233917\/3A-Pie-Chart.png\" alt=\"A pie chart of International Shark Attacks showing 56.2% in the United States, 18.1% in Australia, and 25.7% in other countries\" width=\"555\" height=\"357\" \/><\/p>\n<p>Use the pie chart above to answer the following two questions.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240674\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240674&theme=oea&iframe_resize_id=ohm240674\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q667791\">Hint<\/span><\/p>\n<div id=\"q667791\" class=\"hidden-answer\" style=\"display: none\">Use the key to discover which pie slice represents the percentage of attacks in the U.S.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240675\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240675&theme=oea&iframe_resize_id=ohm240675\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q998027\">Hint<\/span><\/p>\n<div id=\"q998027\" class=\"hidden-answer\" style=\"display: none\">See the recall box for help converting a percent to a count.<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s try one more.\u00a0The following is a pie chart of [latex]387[\/latex] shark attacks in the United States. Use the information from the table to determine how many shark attacks in each of the two categories shown.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1070\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/11234032\/3A-Pie-Chart-2.png\" alt=\"A pie chart of shark attacks in the United States showing 52.5% in Florida and 47.5% in all other states\" width=\"589\" height=\"378\" \/><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240676\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240676&theme=oea&iframe_resize_id=ohm240676\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q216877\">Hint<\/span><\/p>\n<div id=\"q216877\" class=\"hidden-answer\" style=\"display: none\">There were 387 total attacks (given in the text above). See the pie chart key to obtain the necessary percentage. Round to the nearest whole number (up or down).<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240677\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240677&theme=oea&iframe_resize_id=ohm240677\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q17985\">Hint<\/span><\/p>\n<div id=\"q17985\" class=\"hidden-answer\" style=\"display: none\">There were 387 total attacks (given in the text above). See the pie chart key to obtain the necessary percentage. Round to the nearest whole number (up or down).<\/div>\n<\/div>\n<\/div>\n<p>You&#8217;ve seen how to read information presented in frequency tables, bar charts, and pie charts and you&#8217;ve learned to calculate relative frequencies. You&#8217;ve also seen how to interpret the information displayed, and that sometimes it is helpful to convert numbers between ratios, proportions, and percentages in doing so. If you feel comfortable with these skills, then it&#8217;s time to move on to the next section.<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-389-1\">Sharks (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-db346c01b1b3\/downloads\/sharks.csv?ver=1622756678385 <a href=\"#return-footnote-389-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-389","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/389\/revisions"}],"predecessor-version":[{"id":396,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/389\/revisions\/396"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/160"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/389\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=389"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=389"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=389"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}