{"id":146,"date":"2021-10-08T22:59:12","date_gmt":"2021-10-08T22:59:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=146"},"modified":"2022-02-18T22:51:20","modified_gmt":"2022-02-18T22:51:20","slug":"3a-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3a-coreq\/","title":{"raw":"Corequisite Support Activity for Displaying Categorical Data: 3A - 1","rendered":"Corequisite Support Activity for Displaying Categorical Data: 3A &#8211; 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know<\/h3>\r\nIn this support activity you'll become familiar with the following:\r\n<ul>\r\n \t<li><a href=\"#FreqTable\">Read and interpret a frequency table.<\/a><\/li>\r\n \t<li><a href=\"#BarGraph\">Read and interpret a bar graph.<\/a><\/li>\r\n \t<li><a href=\"#PieChart\">Read and interpret a pie chart.<\/a><\/li>\r\n<\/ul>\r\nYou will also have an opportunity to refresh the following skills:\r\n<ul>\r\n \t<li><a href=\"#FractionProportion\">Convert a fraction to a proportion (decimal) and round.<\/a><\/li>\r\n \t<li><a href=\"#ProportionPercent\">Convert a proportion to a percent.<\/a><\/li>\r\n \t<li><a href=\"#PercentNumber\">Given a total, convert a percent of the total into a number.<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the next section of the course material and in the following activity, you will need to read and interpret <strong>frequency tables<\/strong>, <strong>bar graphs<\/strong>, and <strong>pie charts<\/strong>. These kinds of tables, graphs, and charts help us to visualize data collected about a situation in order to understand it clearly. To help you gain familiarity and practice with these ideas before the course section begins, let's work with a small data set to see what methods are available to us for visualizing the data. You'll also need an understanding of percentages and relative frequencies. Look for the recall boxes in the text and\/or refer to the Student Resource pages indicated there if you need a refresher.\r\n<h2>Shark Attacks<\/h2>\r\nIn this corequisite support activity, we will look at shark attacks in the United States and internationally. We will see how visual displays like tables and graphs can help to\u00a0analyze the number of attacks that occur in each country or U. S. state.\r\n\r\n[caption id=\"attachment_2412\" align=\"aligncenter\" width=\"320\"]<img class=\"size-full wp-image-2412\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/31142708\/Carcharodon_carcharias.jpg\" alt=\"a great white shark, swimming, its mouth slightly open\" width=\"320\" height=\"240\" \/> Carcharodon carcharias[\/caption]\r\n\r\nTo frame the landscape for this activity, think about shark attacks for a moment. What areas of the country or the world seem to be associated with a lot of interaction between sharks and humans? What sort of data do you think is collected about location and number of shark attacks? We will examine some data soon; first consider the two questions below.\r\n<p style=\"text-align: center;\"><em>In the United States, which state do you think has the most shark attacks?<\/em><\/p>\r\n<p style=\"text-align: center;\"><em>Which country in the world do you think has the most?\u00a0<\/em><\/p>\r\n<p style=\"text-align: left;\">It's interesting to speculate about the answers to these questions, but can use data to answer them definitively. It will help to organize and visualize the data.\r\n<span id=\"FreqTable\"><\/span><\/p>\r\n\r\n<h3>Frequency tables<\/h3>\r\nFrequency tables include information about a number of times something occurs, also known as the <strong>frequency<\/strong> of occurrences. One column in the table lists different categories or groups. Another column lists the frequency of occurrences associated with each category or group.\r\n\r\nBelow is a frequency table of shark attacks in the United States.[footnote]\u00a0Sharks US only (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from\u00a0https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-\r\ndb346c01b1b3\/downloads\/sharksUS.csv?ver=1622756678385\u00a0[\/footnote]\u00a0A <strong>fre<\/strong><strong>quency table<\/strong> organizes categorical data by listing the different possible categories and the number of times each category occurs in the dataset. For example, in the table below, we see that California had [latex]33[\/latex] shark attacks, Florida had [latex]203[\/latex], and so on.\r\n<div align=\"center\">\r\n<table style=\"width: 349px; height: 161px;\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 462.415px; height: 14px; text-align: center;\" colspan=\"2\"><strong>Shark Attacks in the United States<\/strong><em>\r\n<\/em><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>U.S. State<\/strong><\/td>\r\n<td style=\"width: 219.446px; height: 14px; text-align: center;\"><strong>Count<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>California<\/strong><\/td>\r\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]33[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>Florida<\/strong><\/td>\r\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]203[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>Hawaii<\/strong><\/td>\r\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>North Carolina<\/strong><\/td>\r\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]23[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 230.469px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<td style=\"width: 219.446px; text-align: center;\">[latex]27[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 230.469px; text-align: center;\"><strong>South Carolina<\/strong><\/td>\r\n<td style=\"width: 219.446px; text-align: center;\">[latex]34[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 230.469px; text-align: center;\"><strong>Texas<\/strong><\/td>\r\n<td style=\"width: 219.446px; text-align: center;\">[latex]16[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question]240628[\/ohm_question]\r\n\r\n[reveal-answer q=\"853984\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"853984\"]In the table, find the two highest frequencies of shark attacks and note their associated states.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question]240630[\/ohm_question]\r\n\r\n[reveal-answer q=\"548239\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"548239\"]How many total shark attacks are listed in the table above for all the listed states combined.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question]240668[\/ohm_question]\r\n[reveal-answer q=\"501422\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"501422\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>Relative frequency<\/h3>\r\nThe <strong>relative frequency<\/strong>\u00a0is a proportion or percent of a total frequency. It tells us how frequently a particular value has occurred out of the total number of occurrences. For example, in the table Shark Attacks in the United States, we can see that there were 23 shark attacks in North Carolina out of the 387 shark attacks in all the states combined. If we want to know what proportion of the total attacks occurred in North Carolina, we can express them as a ratio (fraction), then convert the ratio to a proportion (decimal) or a percent.\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{\\text{# attacks in N.C.}}{\\text{# total attacks}}=\\dfrac{23}{387} \\approx 0.0594[\/latex] or about [latex]5.94%[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">We can express the relative frequency by saying either of the following.<\/p>\r\n<p style=\"padding-left: 30px; text-align: center;\"><em style=\"font-size: 1em;\">The proportion of U.S. shark attacks in North Carolina is 0.0594\u00a0<\/em><\/p>\r\n<p style=\"padding-left: 30px; text-align: center;\"><span style=\"font-size: 1em;\"><em>A<\/em><\/span><em style=\"font-size: 1em;\">bout 5.94% of U.S. shark attacks occurred in North Carolina.<\/em><\/p>\r\nFrequency tables commonly include a column for relative frequency, expressed as a proportion (decimal) or a percent. See the Recall box below for a refresher on how to convert fractions to proportions and percentages then complete the missing information in the table below.\r\n<span id=\"FractionProportion\"><\/span><span id=\"ProportionPercent\"><\/span>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nTo write the <strong>relative frequency<\/strong> of an item in a frequency table, divide the frequency (count) of an item by the total frequency of the table.\r\n\r\nEx. Calculate the relative frequency of shark attacks in North Carolina as a proportion rounded to 4 decimal places.\r\n\r\nCore Skill:\r\n[reveal-answer q=\"379767\"]Convert a fraction to a proportion (decimal) and round.[\/reveal-answer]\r\n[hidden-answer a=\"379767\"]\r\n\r\n23 out of the 387 attacks occurred in N.C. We'll write this as [latex]\\dfrac{23}{387}[\/latex].\r\n\r\nTo convert a fraction to a proportion (a decimal), divide the numerator by the denominator using a calculator.\r\n<p style=\"padding-left: 30px;\">[latex]23\\div 387=0.0594315245...[\/latex]<\/p>\r\nTo round a number to a certain number of places, check the number to right of that place.\r\n<p style=\"padding-left: 30px;\">If the number to the right is 0 - 4, keep desired place value the same and drop everything to the right.<\/p>\r\n<p style=\"padding-left: 30px;\">If the number to the right is 5 - 9, round the desired place value up one and drop everything to the right.<\/p>\r\nRound the proportion [latex]0.0594315245...[\/latex] to four decimal places.\r\n<p style=\"padding-left: 30px;\">[latex]0.0594\\fbox{3}...[\/latex] We see that the place to the right of four decimal places includes a 3 so we don't need to round up. We'll keep 0.0594 and drop everything to the right.<\/p>\r\n<strong>The proportion of attacks in North Carolina is 0.0594.<\/strong>\r\n\r\n[\/hidden-answer]\r\n\r\nCore Skill:\r\n[reveal-answer q=\"342198\"]Convert a proportion to a percent.[\/reveal-answer]\r\n[hidden-answer a=\"342198\"]\r\n\r\nTo convert a proportion (decimal) to a percent, multiply the proportion by 100 and append a percent symbol, %.\r\n\r\nEx. The proportion of shark attacks occurring in North Carolina was 0.0594, rounded to 4 decimal places.\r\n<p style=\"padding-left: 30px;\">Multiply this number by 100 and append the percent symbol. To multiply any number by 100, move the decimal two places to the right.<\/p>\r\n<p style=\"padding-left: 30px;\">[latex]0.0594\\times100=5.94[\/latex].<\/p>\r\n<strong>5.94% of all shark attacks occurred in North Carolina.<\/strong>\r\n\r\n[\/hidden-answer]\r\n\r\n<span style=\"background-color: #ffff00;\">[Also see Corequisite Support Activities 1E and 2D for more practice.]\u00a0<\/span>\r\n\r\n<\/div>\r\nRecall that a relative frequency represents the proportion or percentage of a particular frequency out of the total frequency. The table below contains the same information as the one you examined above, but adds columns for\u00a0<em>Proportion<\/em> and <em>Percent\u00a0<\/em>(%). We can see in the table that the proportion of shark attacks that occurred in California out of the total number of shark attacks is 0.0853, which is equivalent to 8.53% of all the shark attacks listed. In the following question, you'll need to compute the missing proportion and percent for the rows <em>Other<\/em>, <em>South Carolina<\/em>, and <em>Texas<\/em>.\r\n<div align=\"center\">\r\n<table style=\"height: 122px;\">\r\n<tbody>\r\n<tr style=\"height: 10px;\">\r\n<td style=\"text-align: center; height: 10px; width: 404.5px;\" colspan=\"4\"><strong>Shark Attacks in the United States<\/strong><strong>\r\n<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>U.S. State<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\"><strong>Count<\/strong><\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><strong>Proportion<\/strong><\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><strong>Percent (%)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>California<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">33<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.0853<\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">8.53<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Florida<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">203<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.5245<\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">52.45<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Hawaii<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">51<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.1318<\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">13.18<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>North Carolina<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">23<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.0594<\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">5.94<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">27<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>South Carolina<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">34<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Texas<\/strong><\/td>\r\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">16<\/td>\r\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\r\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div><\/div>\r\n<div style=\"text-align: left;\"><\/div>\r\n<div style=\"text-align: left;\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question]240669[\/ohm_question]\r\n\r\nComplete the proportion and percent columns of the shark attack table above. Round your answers to four decimal places.\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 25%; text-align: center;\"><strong>U.S. State<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\"><strong>Count<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\"><strong>Proportion<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\"><strong>Percent(%)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 25%; text-align: center;\"><strong>Other<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\">27<\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 25%; text-align: center;\"><strong>South Carolina<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\">34<\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 25%; text-align: center;\"><strong>Texas<\/strong><\/td>\r\n<td style=\"width: 25%; text-align: center;\">16<\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<td style=\"width: 25%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"225903\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"225903\"]See the Recall box above to refresh these skills.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"BarGraph\">Bar graphs<\/h3>\r\nBar graphs are visual displays of data in which the frequency of each category is indicated by the height of a rectangular bar (or the length if the graph is displayed horizontally). The image below displays a\u00a0<span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">a bar graph (also known as a bar chart) of 689 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. We can see in the graph below, for example, that South Carolina and California had similar numbers of attacks, about 35 each, while Hawaii had about 50.<\/span>\r\n<div><\/div>\r\n<div style=\"text-align: left;\">\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\nWhich regions had the highest number of shark attacks?\u00a0<span style=\"background-color: #ffff00;\">I have an issue with this question based on the bar chart and answer provided by DC. Question embedded below is based on what I think would be better.-jw<\/span>\r\n\r\n[ohm_question]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]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]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. For example, let'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 689 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\nKnowing that the total frequency of attacks is 689 and the relative frequency of attacks in Australia is 18.1%, how could we determine the count of the attacks in Australia? This is same as asking the question\u00a0<em>what is 18.1% of 689?<\/em>\u00a0If you need to, use the recall box below to refresh the process for determining what number a certain percent represents in a given total, then find the frequency (the count) of attacks that occurred in Australia.\r\n<span id=\"PercentNumber\"><\/span>\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 23 of the U.S. attacks happened in North Carolina, which represented 5.94% of the total 387 attacks. Let's work backwards to obtain the number 23 given the percent and total.\r\n\r\nEx. Given that 5.94% of 387 attacks occurred in North Carolina, how many attacks is that?\r\n\r\nFirst, we'll need to translate 5.94% into a number. To do so, drop the percent symbol and divide by 100 (move the decimal two places to the left).\u00a05.94% becomes 0.0594.\r\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}=0.0594[\/latex]<\/p>\r\nThen, multiply the total by 0.0594 (5.94%\u00a0<em>of<\/em> 387; 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>5.94% of the total represents about 23 shark attacks.<\/strong>\r\n\r\nWhy did we obtain 22.9878 as our answer rather than 23? Recall that we had rounded the answer to 23\/387 to obtain the proportion 0.0594 and percent 5.94%.\u00a0We've reversed the process we initially applied to write 23\/387 as a percent!\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nDid you find that about 125 attacks happened in Australia?\u00a0[latex]0.181\\times689=124.709[\/latex], which rounds up to 125. Relative frequencies written as percentages are often approximations due to having rounded them to smaller decimal places. For this reason, the percentages don't always add up to exactly 100%, but they will be close.\r\n\r\nNow it's your turn. Use 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]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]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 387 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]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]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.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know<\/h3>\n<p>In this support activity you&#8217;ll become familiar with the following:<\/p>\n<ul>\n<li><a href=\"#FreqTable\">Read and interpret a frequency table.<\/a><\/li>\n<li><a href=\"#BarGraph\">Read and interpret a bar graph.<\/a><\/li>\n<li><a href=\"#PieChart\">Read and interpret a pie chart.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#FractionProportion\">Convert a fraction to a proportion (decimal) and round.<\/a><\/li>\n<li><a href=\"#ProportionPercent\">Convert a proportion to a percent.<\/a><\/li>\n<li><a href=\"#PercentNumber\">Given a total, convert a percent of the total into a number.<\/a><\/li>\n<\/ul>\n<\/div>\n<p>In the next section of the course material and in the following activity, you will need to read and interpret <strong>frequency tables<\/strong>, <strong>bar graphs<\/strong>, and <strong>pie charts<\/strong>. These kinds of tables, graphs, and charts help us to visualize data collected about a situation in order to understand it clearly. To help you gain familiarity and practice with these ideas before the course section begins, let&#8217;s work with a small data set to see what methods are available to us for visualizing the data. You&#8217;ll also need an understanding of percentages and relative frequencies. Look for the recall boxes in the text and\/or refer to the Student Resource pages indicated there if you need a refresher.<\/p>\n<h2>Shark Attacks<\/h2>\n<p>In this corequisite support activity, we will look at shark attacks in the United States and internationally. We will see how visual displays like tables and graphs can help to\u00a0analyze the number of attacks that occur in each country or U. S. state.<\/p>\n<div id=\"attachment_2412\" style=\"width: 330px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2412\" class=\"size-full wp-image-2412\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/31142708\/Carcharodon_carcharias.jpg\" alt=\"a great white shark, swimming, its mouth slightly open\" width=\"320\" height=\"240\" \/><\/p>\n<p id=\"caption-attachment-2412\" class=\"wp-caption-text\">Carcharodon carcharias<\/p>\n<\/div>\n<p>To frame the landscape for this activity, think about shark attacks for a moment. What areas of the country or the world seem to be associated with a lot of interaction between sharks and humans? What sort of data do you think is collected about location and number of shark attacks? We will examine some data soon; first consider the two questions below.<\/p>\n<p style=\"text-align: center;\"><em>In the United States, which state do you think has the most shark attacks?<\/em><\/p>\n<p style=\"text-align: center;\"><em>Which country in the world do you think has the most?\u00a0<\/em><\/p>\n<p style=\"text-align: left;\">It&#8217;s interesting to speculate about the answers to these questions, but can use data to answer them definitively. It will help to organize and visualize the data.<br \/>\n<span id=\"FreqTable\"><\/span><\/p>\n<h3>Frequency tables<\/h3>\n<p>Frequency tables include information about a number of times something occurs, also known as the <strong>frequency<\/strong> of occurrences. One column in the table lists different categories or groups. Another column lists the frequency of occurrences associated with each category or group.<\/p>\n<p>Below is a frequency table of shark attacks in the United States.<a class=\"footnote\" title=\"\u00a0Sharks US only (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from\u00a0https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-\ndb346c01b1b3\/downloads\/sharksUS.csv?ver=1622756678385\u00a0\" id=\"return-footnote-146-1\" href=\"#footnote-146-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\u00a0A <strong>fre<\/strong><strong>quency table<\/strong> organizes categorical data by listing the different possible categories and the number of times each category occurs in the dataset. For example, in the table below, we see that California had [latex]33[\/latex] shark attacks, Florida had [latex]203[\/latex], and so on.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"width: 349px; height: 161px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 462.415px; height: 14px; text-align: center;\" colspan=\"2\"><strong>Shark Attacks in the United States<\/strong><em><br \/>\n<\/em><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>U.S. State<\/strong><\/td>\n<td style=\"width: 219.446px; height: 14px; text-align: center;\"><strong>Count<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>California<\/strong><\/td>\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]33[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>Florida<\/strong><\/td>\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]203[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>Hawaii<\/strong><\/td>\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]51[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 230.469px; height: 14px; text-align: center;\"><strong>North Carolina<\/strong><\/td>\n<td style=\"width: 219.446px; height: 14px; text-align: center;\">[latex]23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 230.469px; text-align: center;\"><strong>Other<\/strong><\/td>\n<td style=\"width: 219.446px; text-align: center;\">[latex]27[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 230.469px; text-align: center;\"><strong>South Carolina<\/strong><\/td>\n<td style=\"width: 219.446px; text-align: center;\">[latex]34[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 230.469px; text-align: center;\"><strong>Texas<\/strong><\/td>\n<td style=\"width: 219.446px; text-align: center;\">[latex]16[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240628\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240628&theme=oea&iframe_resize_id=ohm240628&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q853984\">Hint<\/span><\/p>\n<div id=\"q853984\" class=\"hidden-answer\" style=\"display: none\">In the table, find the two highest frequencies of shark attacks and note their associated states.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240630\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240630&theme=oea&iframe_resize_id=ohm240630&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q548239\">Hint<\/span><\/p>\n<div id=\"q548239\" class=\"hidden-answer\" style=\"display: none\">How many total shark attacks are listed in the table above for all the listed states combined.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240668\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240668&theme=oea&iframe_resize_id=ohm240668&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q501422\">Hint<\/span><\/p>\n<div id=\"q501422\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<h3>Relative frequency<\/h3>\n<p>The <strong>relative frequency<\/strong>\u00a0is a proportion or percent of a total frequency. It tells us how frequently a particular value has occurred out of the total number of occurrences. For example, in the table Shark Attacks in the United States, we can see that there were 23 shark attacks in North Carolina out of the 387 shark attacks in all the states combined. If we want to know what proportion of the total attacks occurred in North Carolina, we can express them as a ratio (fraction), then convert the ratio to a proportion (decimal) or a percent.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{\\text{# attacks in N.C.}}{\\text{# total attacks}}=\\dfrac{23}{387} \\approx 0.0594[\/latex] or about [latex]5.94%[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">We can express the relative frequency by saying either of the following.<\/p>\n<p style=\"padding-left: 30px; text-align: center;\"><em style=\"font-size: 1em;\">The proportion of U.S. shark attacks in North Carolina is 0.0594\u00a0<\/em><\/p>\n<p style=\"padding-left: 30px; text-align: center;\"><span style=\"font-size: 1em;\"><em>A<\/em><\/span><em style=\"font-size: 1em;\">bout 5.94% of U.S. shark attacks occurred in North Carolina.<\/em><\/p>\n<p>Frequency tables commonly include a column for relative frequency, expressed as a proportion (decimal) or a percent. See the Recall box below for a refresher on how to convert fractions to proportions and percentages then complete the missing information in the table below.<br \/>\n<span id=\"FractionProportion\"><\/span><span id=\"ProportionPercent\"><\/span><\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>To write the <strong>relative frequency<\/strong> of an item in a frequency table, divide the frequency (count) of an item by the total frequency of the table.<\/p>\n<p>Ex. Calculate the relative frequency of shark attacks in North Carolina as a proportion rounded to 4 decimal places.<\/p>\n<p>Core Skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q379767\">Convert a fraction to a proportion (decimal) and round.<\/span><\/p>\n<div id=\"q379767\" class=\"hidden-answer\" style=\"display: none\">\n<p>23 out of the 387 attacks occurred in N.C. We&#8217;ll write this as [latex]\\dfrac{23}{387}[\/latex].<\/p>\n<p>To convert a fraction to a proportion (a decimal), divide the numerator by the denominator using a calculator.<\/p>\n<p style=\"padding-left: 30px;\">[latex]23\\div 387=0.0594315245...[\/latex]<\/p>\n<p>To round a number to a certain number of places, check the number to right of that place.<\/p>\n<p style=\"padding-left: 30px;\">If the number to the right is 0 &#8211; 4, keep desired place value the same and drop everything to the right.<\/p>\n<p style=\"padding-left: 30px;\">If the number to the right is 5 &#8211; 9, round the desired place value up one and drop everything to the right.<\/p>\n<p>Round the proportion [latex]0.0594315245...[\/latex] to four decimal places.<\/p>\n<p style=\"padding-left: 30px;\">[latex]0.0594\\fbox{3}...[\/latex] We see that the place to the right of four decimal places includes a 3 so we don&#8217;t need to round up. We&#8217;ll keep 0.0594 and drop everything to the right.<\/p>\n<p><strong>The proportion of attacks in North Carolina is 0.0594.<\/strong><\/p>\n<\/div>\n<\/div>\n<p>Core Skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q342198\">Convert a proportion to a percent.<\/span><\/p>\n<div id=\"q342198\" class=\"hidden-answer\" style=\"display: none\">\n<p>To convert a proportion (decimal) to a percent, multiply the proportion by 100 and append a percent symbol, %.<\/p>\n<p>Ex. The proportion of shark attacks occurring in North Carolina was 0.0594, rounded to 4 decimal places.<\/p>\n<p style=\"padding-left: 30px;\">Multiply this number by 100 and append the percent symbol. To multiply any number by 100, move the decimal two places to the right.<\/p>\n<p style=\"padding-left: 30px;\">[latex]0.0594\\times100=5.94[\/latex].<\/p>\n<p><strong>5.94% of all shark attacks occurred in North Carolina.<\/strong><\/p>\n<\/div>\n<\/div>\n<p><span style=\"background-color: #ffff00;\">[Also see Corequisite Support Activities 1E and 2D for more practice.]\u00a0<\/span><\/p>\n<\/div>\n<p>Recall that a relative frequency represents the proportion or percentage of a particular frequency out of the total frequency. The table below contains the same information as the one you examined above, but adds columns for\u00a0<em>Proportion<\/em> and <em>Percent\u00a0<\/em>(%). We can see in the table that the proportion of shark attacks that occurred in California out of the total number of shark attacks is 0.0853, which is equivalent to 8.53% of all the shark attacks listed. In the following question, you&#8217;ll need to compute the missing proportion and percent for the rows <em>Other<\/em>, <em>South Carolina<\/em>, and <em>Texas<\/em>.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"height: 122px;\">\n<tbody>\n<tr style=\"height: 10px;\">\n<td style=\"text-align: center; height: 10px; width: 404.5px;\" colspan=\"4\"><strong>Shark Attacks in the United States<\/strong><strong><br \/>\n<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>U.S. State<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\"><strong>Count<\/strong><\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><strong>Proportion<\/strong><\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><strong>Percent (%)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>California<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">33<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.0853<\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">8.53<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Florida<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">203<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.5245<\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">52.45<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Hawaii<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">51<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.1318<\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">13.18<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>North Carolina<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">23<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\">0.0594<\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\">5.94<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Other<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">27<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>South Carolina<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">34<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 119.266px; text-align: center;\"><strong>Texas<\/strong><\/td>\n<td style=\"height: 14px; width: 54.5625px; text-align: center;\">16<\/td>\n<td style=\"height: 14px; width: 93.125px; text-align: center;\"><\/td>\n<td style=\"height: 14px; width: 100.047px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<div style=\"text-align: left;\"><\/div>\n<div style=\"text-align: left;\">\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240669\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240669&theme=oea&iframe_resize_id=ohm240669&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>Complete the proportion and percent columns of the shark attack table above. Round your answers to four decimal places.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><strong>U.S. State<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\"><strong>Count<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\"><strong>Proportion<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\"><strong>Percent(%)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><strong>Other<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\">27<\/td>\n<td style=\"width: 25%;\"><\/td>\n<td style=\"width: 25%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><strong>South Carolina<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\">34<\/td>\n<td style=\"width: 25%;\"><\/td>\n<td style=\"width: 25%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%; text-align: center;\"><strong>Texas<\/strong><\/td>\n<td style=\"width: 25%; text-align: center;\">16<\/td>\n<td style=\"width: 25%;\"><\/td>\n<td style=\"width: 25%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q225903\">Hint<\/span><\/p>\n<div id=\"q225903\" class=\"hidden-answer\" style=\"display: none\">See the Recall box above to refresh these skills.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"BarGraph\">Bar graphs<\/h3>\n<p>Bar graphs are visual displays of data in which the frequency of each category is indicated by the height of a rectangular bar (or the length if the graph is displayed horizontally). The image below displays a\u00a0<span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">a bar graph (also known as a bar chart) of 689 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-146-2\" href=\"#footnote-146-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/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. We can see in the graph below, for example, that South Carolina and California had similar numbers of attacks, about 35 each, while Hawaii had about 50.<\/span><\/p>\n<div><\/div>\n<div style=\"text-align: left;\">\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>Which regions had the highest number of shark attacks?\u00a0<span style=\"background-color: #ffff00;\">I have an issue with this question based on the bar chart and answer provided by DC. Question embedded below is based on what I think would be better.-jw<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm240678\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240678&theme=oea&iframe_resize_id=ohm240678&show_question_numbers\" 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&show_question_numbers\" 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&show_question_numbers\" 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. For example, 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 689 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>Knowing that the total frequency of attacks is 689 and the relative frequency of attacks in Australia is 18.1%, how could we determine the count of the attacks in Australia? This is same as asking the question\u00a0<em>what is 18.1% of 689?<\/em>\u00a0If you need to, use the recall box below to refresh the process for determining what number a certain percent represents in a given total, then find the frequency (the count) of attacks that occurred in Australia.<br \/>\n<span id=\"PercentNumber\"><\/span><\/p>\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 23 of the U.S. attacks happened in North Carolina, which represented 5.94% of the total 387 attacks. Let&#8217;s work backwards to obtain the number 23 given the percent and total.<\/p>\n<p>Ex. Given that 5.94% of 387 attacks occurred in North Carolina, how many attacks is that?<\/p>\n<p>First, we&#8217;ll need to translate 5.94% into a number. To do so, drop the percent symbol and divide by 100 (move the decimal two places to the left).\u00a05.94% becomes 0.0594.<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\dfrac{5.94}{100}=0.0594[\/latex]<\/p>\n<p>Then, multiply the total by 0.0594 (5.94%\u00a0<em>of<\/em> 387; 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>5.94% of the total represents about 23 shark attacks.<\/strong><\/p>\n<p>Why did we obtain 22.9878 as our answer rather than 23? Recall that we had rounded the answer to 23\/387 to obtain the proportion 0.0594 and percent 5.94%.\u00a0We&#8217;ve reversed the process we initially applied to write 23\/387 as a percent!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Did you find that about 125 attacks happened in Australia?\u00a0[latex]0.181\\times689=124.709[\/latex], which rounds up to 125. Relative frequencies written as percentages are often approximations due to having rounded them to smaller decimal places. For this reason, the percentages don&#8217;t always add up to exactly 100%, but they will be close.<\/p>\n<p>Now it&#8217;s your turn. 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&show_question_numbers\" 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&show_question_numbers\" 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 387 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&show_question_numbers\" 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&show_question_numbers\" 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<\/div>\n<\/div>\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-146\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">Public domain content<\/div><ul class=\"citation-list\"><li>Great White Shark. <strong>Authored by<\/strong>: Sharkdiver68. <strong>Provided by<\/strong>: Wikimedia Commons. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Carcharodon_carcharias.jpg\">https:\/\/commons.wikimedia.org\/wiki\/File:Carcharodon_carcharias.jpg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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-146-1\">\u00a0Sharks US only (csv). (n.d.). The Art &amp; Science of Learning from Data. Retrieved from\u00a0https:\/\/img1.wsimg.com\/blobby\/go\/bbca5dba-4947-4587-b40a-\r\ndb346c01b1b3\/downloads\/sharksUS.csv?ver=1622756678385\u00a0 <a href=\"#return-footnote-146-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-146-2\">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-146-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\"Great White Shark\",\"author\":\"Sharkdiver68\",\"organization\":\"Wikimedia Commons\",\"url\":\"https:\/\/commons.wikimedia.org\/wiki\/File:Carcharodon_carcharias.jpg\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-146","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":90,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/146\/revisions"}],"predecessor-version":[{"id":3376,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/146\/revisions\/3376"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/146\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=146"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=146"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=146"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}