{"id":231,"date":"2022-02-18T23:31:35","date_gmt":"2022-02-18T23:31:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=231"},"modified":"2022-03-29T21:38:07","modified_gmt":"2022-03-29T21:38:07","slug":"applications-of-bar-graphs-corequisite-support-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/applications-of-bar-graphs-corequisite-support-activity\/","title":{"raw":"Applications of Bar Graphs: Corequisite Support Activity","rendered":"Applications of Bar Graphs: Corequisite Support Activity"},"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=\"#BarPercent\">Read and interpret bar charts that represent percentages.<\/a><\/li>\r\n \t<li><a href=\"#Stacked\">Read and interpret stacked bar charts.<\/a><\/li>\r\n \t<li><a href=\"#AbsPercent\">Express absolute change in percentages.<\/a><\/li>\r\n \t<li><a href=\"#RelPercent\">Express relative change in percentages.<\/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=\"#RecallAbs\">Compute absolute change between two values.<\/a><\/li>\r\n \t<li><a href=\"#RecallRel\">Compute relative change between two values.<\/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 be able to interpret data presented in side-by-side and stacked bar charts. Prepare for that in this support activity by practicing working with data presented as percentages. At the end of the activity you'll also compute absolute and relative changes in percentages. That part can be tricky. Follow the Recall box and question hints for help along the way. You may also wish to refer to\u00a0<strong><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\" target=\"_blank\" rel=\"noopener\">Fractions, Decimals, Percentages.<\/a><\/strong>\r\n<h2 id=\"BarPercent\"><strong>Bar Charts<\/strong><\/h2>\r\nYou worked with bar graphs (also called bar charts) recently in <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3a\/\">What to Know About Displaying Categorical Data: 3A.<\/a> The graphs in that page displayed several bars, each representing a different categorical variable. The height of the bar represented that category's associated frequency (count). The graphs we'll look at in this activity are similar to the ones you saw there, but instead of the bar heights representing counts, these will represent percentages. Let's take a close look at the first graph below, Age Distribution of At-Home Workers, as an example.\r\n<div class=\"textbox exercises\">\r\n<h3>interactive example<\/h3>\r\n[reveal-answer q=\"418269\"]Age Distribution of At-Home Workers[\/reveal-answer]\r\n[hidden-answer a=\"418269\"]\r\n\r\n<img class=\"alignnone wp-image-1409 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17201737\/3B-1.png\" alt=\"The bar graph is titled &quot;Age Distribution of At-Home Workers&quot;. The x-axis organizes the age groups, and the y-axis is labeled &quot;Percentage&quot;. The age groups are distributed as follows: 15-24 years (5%), 25-34 years (14%), 35-44 years (23%), 45-54 years (27%), 55-64 years (22%), 65 years and over (10%).\" width=\"1024\" height=\"560\" \/>[\/hidden-answer]\r\n<ol>\r\n \t<li>According to the graph, what percent of at-home workers were\u00a0[latex]15[\/latex] to [latex]24[\/latex] years old?<\/li>\r\n \t<li>Which age range of workers makes up nearly [latex]15\\%[\/latex] of at-home workers?<\/li>\r\n \t<li>What percent of at-home workers are at least [latex]65[\/latex] years old?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"655838\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"655838\"]\r\n<ol>\r\n \t<li>We can see from the graph that workers who were [latex]15[\/latex] to [latex]24[\/latex] years old represented [latex]5\\%[\/latex] of all at-home workers.<\/li>\r\n \t<li>Workers aged [latex]25[\/latex] to [latex]34[\/latex] years old represented nearly [latex]15\\%[\/latex] of at-home workers.<\/li>\r\n \t<li>Workers at least [latex]65[\/latex] years old make up [latex]10\\%[\/latex] of at-home workers.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe graph below shows data from the U.S. Census Bureau on at-home workers in the United States in 2010. [footnote] Mateyka, P. J., Rapino, M. A., &amp; Landivar, L. C. (2012, October). Home-based workers in the United States: 2010. United States Census Bureau. https:\/\/www.census.gov\/prod\/2012pubs\/p70-132.pdf [\/footnote] Note that age ranges are listed along the horizontal axis and percentages are marked along the vertical axis. The graph displays the percentages of all workers, separated by age ranges, who worked at home at least one full day during a typical work week in 2010 (<em>at-home workers<\/em>)<em>.<\/em>\r\n\r\n<img class=\"alignnone wp-image-1409 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17201737\/3B-1.png\" alt=\"The bar graph is titled &quot;Age Distribution of At-Home Workers&quot;. The x-axis organizes the age groups, and the y-axis is labeled &quot;Percentage&quot;. The age groups are distributed as follows: 15-24 years (5%), 25-34 years (14%), 35-44 years (23%), 45-54 years (27%), 55-64 years (22%), 65 years and over (10%).\" width=\"1024\" height=\"560\" \/>\r\n\r\nUse this graph to answer the questions below.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240790[\/ohm_question]\r\n\r\n[reveal-answer q=\"183513\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"183513\"]Refer to the bar graph (the chart) above.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240989[\/ohm_question]\r\n\r\n[reveal-answer q=\"140683\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"140683\"]Note that percentages are marked along the vertical axis of the graph.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]240791[\/ohm_question]\r\n\r\n[reveal-answer q=\"876290\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"876290\"]Be sure to include all the age ranges up to and including workers [latex]44[\/latex] years of age or younger. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240792[\/ohm_question]\r\n\r\n[reveal-answer q=\"773223\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"773223\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"Stacked\"><strong>Stacked Bar Charts<\/strong><\/h3>\r\nStacked bar charts also display values for different categories but rather than showing a different bar for each category, they display sub-categories as segments within each bar. Sometimes the bars represent counts, while others, such as the one we see in the image below, display percentages. Each segment represents a percentage of the whole so it's easy to see relative differences within a bar. But as segment percentages grow smaller, it becomes difficult to estimate them. Let's take a look at the graph below to gain a better understanding of how to read stacked bar charts.\r\n\r\n<img class=\"alignnone wp-image-1410 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17202149\/3B-2.png\" alt=\"A vertical stacked bar chart of expected oral cavity and pharynx cancers in 2018. The vertical axis has percentages in increments of 10 going up to 100. At the bottom is a legend showing that blue indicates tongue, orange indicates mouth, gray indicates pharynx, and yellow indicates other oral cavity. For the &quot;Number of New Cases,&quot; the blue section reaches from the bottom to just over 30%, the orange from there nearly to 60%, the gray from there to about a third of the way between 90% and 100%, and the yellow the rest of the way to 100%. For &quot;Estimated Deaths,&quot; the blue section reaches from the bottom to about halfway between 20% and 30%, the orange from there to just over 50%, the gray from there to about one third of the way between 80% and 90%, and the yellow from there the rest of the way to 100%.\" width=\"1024\" height=\"817\" \/>\r\n\r\nThe graph above shows the expected number of new cases of oral cavity and pharynx cancer for 2018 and the expected number of deaths from oral cavity and pharynx cancer for 2018, separated by the specific location of the cancer. [footnote] American Cancer Society. (2018). Table 1. Estimated number of new cancer cases and deaths by sex, US, 2018. https:\/\/www.cancer.org\/content\/dam\/cancer-org\/research\/cancer-facts-and-statistics\/annual-cancer-facts-and-figures\/2018\/estimated-number-of-new-cancer-cases-and-deaths-by-sex-us-2018.pdf. [\/footnote] The bar on the left shows the number of new cases of a cancer by location in the body as a percent of all new oral cavity and pharynx cancers that year. The bar on the right shows the number of deaths by location of cancer as a percent of total deaths from these cancers. The percentages represented by the segments within each bar will total to [latex]100[\/latex]%. For example, we can see that in the bar on the left, the yellow segment covers about [latex]7[\/latex]% of the bar from [latex]93[\/latex]% to [latex]100[\/latex]%. This means that locations other than tongue, mouth, or pharynx accounted for about [latex]7[\/latex]% of new cancers. In the bar on the right, we see that deaths from cancers in other locations accounted for about [latex]17[\/latex]% of new cancers (the yellow segment covers from about [latex]83[\/latex]% to [latex]100[\/latex]%).\r\n<div class=\"textbox exercises\">\r\n<h3>interactive Example<\/h3>\r\nWhat percent of estimated deaths from these cancer were located in the tongue? In the mouth? In the pharynx? Estimate them by looking at the range of percentages covered by each segment. Check your answers, then complete the question below the graph.\r\n\r\n[reveal-answer q=\"554516\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"554516\"]\r\n\r\nOf the estimated deaths from oral cavity and pharynx cancers in 2018:\r\n<ul>\r\n \t<li>[latex]25[\/latex]% were located in the tongue<\/li>\r\n \t<li>[latex]26[\/latex]% were located in the mouth<\/li>\r\n \t<li>[latex]32[\/latex]% were located in the pharynx<\/li>\r\n \t<li>[latex]17[\/latex]% were located in some other oral cavity.<\/li>\r\n<\/ul>\r\nIt appears that the blue segment covers the bottom [latex]25[\/latex]% of the graph, the orange about [latex]26[\/latex]% (from [latex]25[\/latex]% to [latex]51[\/latex]%), and the grey covers about [latex]32[\/latex]% (from [latex]51[\/latex]% to [latex]83[\/latex]%). Together with the [latex]17[\/latex]% covered by the yellow segment, that makes [latex]100[\/latex]%.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn to practice reading the stacked bar chart by answering the following questions. The graph is linked again here for convenience.\u00a0[reveal-answer q=\"446591\"]Click here to open the graph: Expected Oral Cavity &amp; Pharynx Cancers in 2018[\/reveal-answer]\r\n[hidden-answer a=\"446591\"]\r\n\r\n<img class=\"alignnone wp-image-1410 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17202149\/3B-2.png\" alt=\"A vertical stacked bar chart of expected oral cavity and pharynx cancers in 2018. The vertical axis has percentages in increments of 10 going up to 100. At the bottom is a legend showing that blue indicates tongue, orange indicates mouth, gray indicates pharynx, and yellow indicates other oral cavity. For the &quot;Number of New Cases,&quot; the blue section reaches from the bottom to just over 30%, the orange from there nearly to 60%, the gray from there to about a third of the way between 90% and 100%, and the yellow the rest of the way to 100%. For &quot;Estimated Deaths,&quot; the blue section reaches from the bottom to about halfway between 20% and 30%, the orange from there to just over 50%, the gray from there to about one third of the way between 80% and 90%, and the yellow from there the rest of the way to 100%.\" width=\"1024\" height=\"817\" \/>\r\n\r\n[\/hidden-answer]\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240991[\/ohm_question]\r\n\r\n[reveal-answer q=\"330314\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"330314\"]See the paragraph above the graph for guidance if needed.[\/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]240994[\/ohm_question]\r\n\r\n[reveal-answer q=\"282916\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"282916\"]See the paragraph above the graph for guidance if needed.[\/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]240996[\/ohm_question]\r\n\r\n[reveal-answer q=\"251689\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"251689\"]See the key for a description.[\/hidden-answer]\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]240794[\/ohm_question]\r\n\r\n[reveal-answer q=\"212822\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"212822\"]Remember that the total percentages of each segment add up to [latex]100[\/latex]%[\/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]240795[\/ohm_question]\r\n\r\n[reveal-answer q=\"270540\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"270540\"]Remember that the total percentages of each segment add up to [latex]100[\/latex]%[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><strong>Changes in Percentages<\/strong><\/h3>\r\nWhen examining data, it can sometimes be helpful to compare two values by taking their absolute change or their relative change.\u00a0It can be challenging, though, to compare relative change when data are presented as percentages. Before we try to understand how to apply these comparisons to percentages, please refresh your understanding of absolute and relative difference in the Recall box below.\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nWhen computing absolute change and relative change between two values, we need one value that we think of as the starting point and the other that represents the value after some change. We'll call the starting point value the\u00a0<strong>reference value<\/strong> and the second one will be the\u00a0<strong>new value<\/strong>. We'll use these terms in the skill explanations below.\r\n\r\n<span id=\"RecallAbs\">Core skill:<\/span>\r\n[reveal-answer q=\"754599\"]Compute absolute change between two values[\/reveal-answer]\r\n[hidden-answer a=\"754599\"]\r\n\r\nThe\u00a0<strong>absolute change<\/strong> between two values indicates the actual increase or decrease from one value to the next.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]\\text{absolute change }=\\text{new value }-\\text{reference value}[\/latex]<\/p>\r\n&nbsp;\r\n\r\nAbsolute change retains the units on the two values. For example a decrease in value from $[latex]15,000[\/latex] to $[latex]12,000[\/latex] is expressed in dollars.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]12,000\\text{ dollars } -15,000\\text{ dollars }=-3000\\text{ dollars }[\/latex]<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong><em>The value decreased [latex]3,000[\/latex] dollars.\u00a0<\/em><\/strong><\/p>\r\n&nbsp;\r\n\r\n<hr \/>\r\n\r\n<strong>When using percentage points as the unit, the absolute change is expressed in percentage points.<\/strong>\r\n\r\nEx. A survey indicates that [latex]50[\/latex]% of dentists polled would recommend a toothpaste. After the company improves the toothpaste, a new survey indicates that [latex]80[\/latex]% of dentists polled would recommend it.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]80\\text{ percentage points } -50\\text{ percentage points }=30\\text{ percentage points }[\/latex]<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong><em>The number of dentists who recommend the toothpaste increased [latex]30[\/latex] percentage points.<\/em><\/strong><\/p>\r\n&nbsp;\r\n\r\n<hr \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<span id=\"RecallRel\">Core skill:<\/span>\r\n[reveal-answer q=\"434757\"]Compute relative change between two values[\/reveal-answer]\r\n[hidden-answer a=\"434757\"]\r\n\r\nThe\u00a0<strong>relative change<\/strong> between two values is a ratio that expresses the absolute change between two values relative to the reference value.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]\\dfrac{\\text{absolute change}}{\\text{reference value}}=\\dfrac{\\text{new value }-\\text{reference value}}{\\text{reference value}}[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThe relative change in two values is unitless, since the units cancel from the numerator to the denominator.\u00a0We can express relative change as a percentage by multiplying by [latex]100[\/latex]%.\r\n\r\n&nbsp;\r\n\r\nEx.\u00a0For example, the relative change in value from $[latex]15,000[\/latex] to $[latex]12,000[\/latex] is unitless, but may be expressed as a percentage.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(12,000-15,000\\right)\\text{ dollars }}{15,000\\text{ dollars }}=\\dfrac{-3,000 \\cancel{\\text{ dollars} }}{15,000\\cancel{\\text{ dollars} }}=-\\dfrac{1}{5}=-0.20\\times100\\%=-20\\%[\/latex]<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong><em>The value decreased [latex]20[\/latex]%.\u00a0<\/em><\/strong><\/p>\r\n&nbsp;\r\n\r\n<hr \/>\r\n\r\n<strong>When using percentage points as the unit, the relative change is unitless, but may be expressed as a percentage.<\/strong>\r\n\r\n&nbsp;\r\n\r\nEx. A survey indicated that [latex]50[\/latex]% of dentists polled would recommend a toothpaste. After the company improved the toothpaste, a new survey indicated that [latex]80[\/latex]% of dentists polled would recommend it.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(80-50\\right)\\text{ percentage points }}{50\\text{ percentage points }}=\\dfrac{30\\cancel{\\text{ percentage points} } }{50\\cancel{\\text{ percentage points} } }=\\dfrac{3}{5}=0.6\\times100\\%=60\\%[\/latex]<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><em><strong>The number of dentists who would recommend the toothpaste increased [latex]60[\/latex]%.<\/strong>\r\n<\/em><\/p>\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIt can be tricky to handle the units when they are in percentage points. Use this rule of thumb when\u00a0the original units are percentage points:\r\n<ul>\r\n \t<li id=\"AbsPercent\">The <strong>absolute difference<\/strong> will be in percentage points, indicating the change occurred in a number of percentage points.<\/li>\r\n \t<li id=\"RelPercent\">The <strong>relative difference<\/strong> will be expressed with the [latex]\\%[\/latex] symbol, indicating that the amount of something has changed by some percent relative to its original amount.<\/li>\r\n<\/ul>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConsider a small town that suffered the downsizing of a large manufacturing plant. In 2010, [latex]60[\/latex]% of the town's workers were employed in the plant. But in 2011, only [latex]27[\/latex]% of the town's workers remained.\r\n\r\nWhat was the absolute change in the percentage of workers employed at the plant?\r\n\r\n[reveal-answer q=\"583613\"]Show Solution[\/reveal-answer][hidden-answer a=\"583613\"]\r\n<p style=\"text-align: center;\">[latex]27\\text{ percentage points } -60\\text{ percentage points }=-33\\text{ percentage points }[\/latex]<\/p>\r\n<p style=\"text-align: center;\"><strong><em>The number of workers from the town who worked at the plant decreased [latex]33[\/latex] percentage points.<\/em><\/strong><\/p>\r\n[\/hidden-answer]\r\n\r\nWhat was the relative change?\r\n\r\n[reveal-answer q=\"646464\"]Show Solution[\/reveal-answer]\r\n<p style=\"text-align: left;\">[hidden-answer a=\"646464\"]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(27-60\\right)\\text{ percentage points }}{60\\text{ percentage points }}=\\dfrac{-33\\cancel{\\text{ percentage points} } }{60\\cancel{\\text{ percentage points} } }=-\\dfrac{11}{20}=-0.55\\times100\\%=-55\\%[\/latex]<\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><em><strong>The number of workers from the town who worked at the plant decreased [latex]55[\/latex]%.<\/strong><\/em><\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you try this scenario about graduation rates.\r\n\r\nIn 2013, [latex]80[\/latex]% of the original class of 2013 (who started in 2009) graduated from Valley High School, and in 2014, [latex]73[\/latex]% of the original class of 2014 graduated.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]240797[\/ohm_question]\r\n\r\n[reveal-answer q=\"818757\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"818757\"]Begin with the percentage from 2014.[\/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]240798[\/ohm_question]\r\n\r\n[reveal-answer q=\"220308\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"220308\"]See the recall box above for details.\u00a0 [latex]\\text{relative change }=\\dfrac{\\text{absolute change}}{\\text{reference value}}=\\dfrac{\\text{new value }-\\text{reference value}}{\\text{reference value}}\\times100\\%[\/latex], where the\u00a0<em>reference value<\/em> is the starting value.<span style=\"font-size: 1rem; text-align: initial; background-color: initial;\">[\/hidden-answer]<\/span>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]240800[\/ohm_question]\r\n\r\n[reveal-answer q=\"55079\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"55079\"]What do <em>you<\/em> think? Have you been given any information about a number of students in either class?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div>Now that you've gained some experience reading and interpreting graphs that represent percentages, it's time to move on to the next section and activity.<\/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=\"#BarPercent\">Read and interpret bar charts that represent percentages.<\/a><\/li>\n<li><a href=\"#Stacked\">Read and interpret stacked bar charts.<\/a><\/li>\n<li><a href=\"#AbsPercent\">Express absolute change in percentages.<\/a><\/li>\n<li><a href=\"#RelPercent\">Express relative change in percentages.<\/a><\/li>\n<\/ul>\n<p>You will also have an opportunity to refresh the following skills:<\/p>\n<ul>\n<li><a href=\"#RecallAbs\">Compute absolute change between two values.<\/a><\/li>\n<li><a href=\"#RecallRel\">Compute relative change between two values.<\/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 be able to interpret data presented in side-by-side and stacked bar charts. Prepare for that in this support activity by practicing working with data presented as percentages. At the end of the activity you&#8217;ll also compute absolute and relative changes in percentages. That part can be tricky. Follow the Recall box and question hints for help along the way. You may also wish to refer to\u00a0<strong><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\" target=\"_blank\" rel=\"noopener\">Fractions, Decimals, Percentages.<\/a><\/strong><\/p>\n<h2 id=\"BarPercent\"><strong>Bar Charts<\/strong><\/h2>\n<p>You worked with bar graphs (also called bar charts) recently in <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/3a\/\">What to Know About Displaying Categorical Data: 3A.<\/a> The graphs in that page displayed several bars, each representing a different categorical variable. The height of the bar represented that category&#8217;s associated frequency (count). The graphs we&#8217;ll look at in this activity are similar to the ones you saw there, but instead of the bar heights representing counts, these will represent percentages. Let&#8217;s take a close look at the first graph below, Age Distribution of At-Home Workers, as an example.<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive example<\/h3>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q418269\">Age Distribution of At-Home Workers<\/span><\/p>\n<div id=\"q418269\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1409 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17201737\/3B-1.png\" alt=\"The bar graph is titled &quot;Age Distribution of At-Home Workers&quot;. The x-axis organizes the age groups, and the y-axis is labeled &quot;Percentage&quot;. The age groups are distributed as follows: 15-24 years (5%), 25-34 years (14%), 35-44 years (23%), 45-54 years (27%), 55-64 years (22%), 65 years and over (10%).\" width=\"1024\" height=\"560\" \/><\/div>\n<\/div>\n<ol>\n<li>According to the graph, what percent of at-home workers were\u00a0[latex]15[\/latex] to [latex]24[\/latex] years old?<\/li>\n<li>Which age range of workers makes up nearly [latex]15\\%[\/latex] of at-home workers?<\/li>\n<li>What percent of at-home workers are at least [latex]65[\/latex] years old?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q655838\">Show Answer<\/span><\/p>\n<div id=\"q655838\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>We can see from the graph that workers who were [latex]15[\/latex] to [latex]24[\/latex] years old represented [latex]5\\%[\/latex] of all at-home workers.<\/li>\n<li>Workers aged [latex]25[\/latex] to [latex]34[\/latex] years old represented nearly [latex]15\\%[\/latex] of at-home workers.<\/li>\n<li>Workers at least [latex]65[\/latex] years old make up [latex]10\\%[\/latex] of at-home workers.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>The graph below shows data from the U.S. Census Bureau on at-home workers in the United States in 2010. <a class=\"footnote\" title=\"Mateyka, P. J., Rapino, M. A., &amp; Landivar, L. C. (2012, October). Home-based workers in the United States: 2010. United States Census Bureau. https:\/\/www.census.gov\/prod\/2012pubs\/p70-132.pdf\" id=\"return-footnote-231-1\" href=\"#footnote-231-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Note that age ranges are listed along the horizontal axis and percentages are marked along the vertical axis. The graph displays the percentages of all workers, separated by age ranges, who worked at home at least one full day during a typical work week in 2010 (<em>at-home workers<\/em>)<em>.<\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1409 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17201737\/3B-1.png\" alt=\"The bar graph is titled &quot;Age Distribution of At-Home Workers&quot;. The x-axis organizes the age groups, and the y-axis is labeled &quot;Percentage&quot;. The age groups are distributed as follows: 15-24 years (5%), 25-34 years (14%), 35-44 years (23%), 45-54 years (27%), 55-64 years (22%), 65 years and over (10%).\" width=\"1024\" height=\"560\" \/><\/p>\n<p>Use this graph to answer the questions below.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240790\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240790&theme=oea&iframe_resize_id=ohm240790\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q183513\">Hint<\/span><\/p>\n<div id=\"q183513\" class=\"hidden-answer\" style=\"display: none\">Refer to the bar graph (the chart) above.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240989\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240989&theme=oea&iframe_resize_id=ohm240989\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q140683\">Hint<\/span><\/p>\n<div id=\"q140683\" class=\"hidden-answer\" style=\"display: none\">Note that percentages are marked along the vertical axis of the graph.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240791\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240791&theme=oea&iframe_resize_id=ohm240791\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q876290\">Hint<\/span><\/p>\n<div id=\"q876290\" class=\"hidden-answer\" style=\"display: none\">Be sure to include all the age ranges up to and including workers [latex]44[\/latex] years of age or younger. <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240792\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240792&theme=oea&iframe_resize_id=ohm240792\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q773223\">Hint<\/span><\/p>\n<div id=\"q773223\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<h3 id=\"Stacked\"><strong>Stacked Bar Charts<\/strong><\/h3>\n<p>Stacked bar charts also display values for different categories but rather than showing a different bar for each category, they display sub-categories as segments within each bar. Sometimes the bars represent counts, while others, such as the one we see in the image below, display percentages. Each segment represents a percentage of the whole so it&#8217;s easy to see relative differences within a bar. But as segment percentages grow smaller, it becomes difficult to estimate them. Let&#8217;s take a look at the graph below to gain a better understanding of how to read stacked bar charts.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1410 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17202149\/3B-2.png\" alt=\"A vertical stacked bar chart of expected oral cavity and pharynx cancers in 2018. The vertical axis has percentages in increments of 10 going up to 100. At the bottom is a legend showing that blue indicates tongue, orange indicates mouth, gray indicates pharynx, and yellow indicates other oral cavity. For the &quot;Number of New Cases,&quot; the blue section reaches from the bottom to just over 30%, the orange from there nearly to 60%, the gray from there to about a third of the way between 90% and 100%, and the yellow the rest of the way to 100%. For &quot;Estimated Deaths,&quot; the blue section reaches from the bottom to about halfway between 20% and 30%, the orange from there to just over 50%, the gray from there to about one third of the way between 80% and 90%, and the yellow from there the rest of the way to 100%.\" width=\"1024\" height=\"817\" \/><\/p>\n<p>The graph above shows the expected number of new cases of oral cavity and pharynx cancer for 2018 and the expected number of deaths from oral cavity and pharynx cancer for 2018, separated by the specific location of the cancer. <a class=\"footnote\" title=\"American Cancer Society. (2018). Table 1. Estimated number of new cancer cases and deaths by sex, US, 2018. https:\/\/www.cancer.org\/content\/dam\/cancer-org\/research\/cancer-facts-and-statistics\/annual-cancer-facts-and-figures\/2018\/estimated-number-of-new-cancer-cases-and-deaths-by-sex-us-2018.pdf.\" id=\"return-footnote-231-2\" href=\"#footnote-231-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> The bar on the left shows the number of new cases of a cancer by location in the body as a percent of all new oral cavity and pharynx cancers that year. The bar on the right shows the number of deaths by location of cancer as a percent of total deaths from these cancers. The percentages represented by the segments within each bar will total to [latex]100[\/latex]%. For example, we can see that in the bar on the left, the yellow segment covers about [latex]7[\/latex]% of the bar from [latex]93[\/latex]% to [latex]100[\/latex]%. This means that locations other than tongue, mouth, or pharynx accounted for about [latex]7[\/latex]% of new cancers. In the bar on the right, we see that deaths from cancers in other locations accounted for about [latex]17[\/latex]% of new cancers (the yellow segment covers from about [latex]83[\/latex]% to [latex]100[\/latex]%).<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive Example<\/h3>\n<p>What percent of estimated deaths from these cancer were located in the tongue? In the mouth? In the pharynx? Estimate them by looking at the range of percentages covered by each segment. Check your answers, then complete the question below the graph.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q554516\">Show Solution<\/span><\/p>\n<div id=\"q554516\" class=\"hidden-answer\" style=\"display: none\">\n<p>Of the estimated deaths from oral cavity and pharynx cancers in 2018:<\/p>\n<ul>\n<li>[latex]25[\/latex]% were located in the tongue<\/li>\n<li>[latex]26[\/latex]% were located in the mouth<\/li>\n<li>[latex]32[\/latex]% were located in the pharynx<\/li>\n<li>[latex]17[\/latex]% were located in some other oral cavity.<\/li>\n<\/ul>\n<p>It appears that the blue segment covers the bottom [latex]25[\/latex]% of the graph, the orange about [latex]26[\/latex]% (from [latex]25[\/latex]% to [latex]51[\/latex]%), and the grey covers about [latex]32[\/latex]% (from [latex]51[\/latex]% to [latex]83[\/latex]%). Together with the [latex]17[\/latex]% covered by the yellow segment, that makes [latex]100[\/latex]%.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now it&#8217;s your turn to practice reading the stacked bar chart by answering the following questions. The graph is linked again here for convenience.\u00a0<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q446591\">Click here to open the graph: Expected Oral Cavity &amp; Pharynx Cancers in 2018<\/span><\/p>\n<div id=\"q446591\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1410 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2021\/10\/17202149\/3B-2.png\" alt=\"A vertical stacked bar chart of expected oral cavity and pharynx cancers in 2018. The vertical axis has percentages in increments of 10 going up to 100. At the bottom is a legend showing that blue indicates tongue, orange indicates mouth, gray indicates pharynx, and yellow indicates other oral cavity. For the &quot;Number of New Cases,&quot; the blue section reaches from the bottom to just over 30%, the orange from there nearly to 60%, the gray from there to about a third of the way between 90% and 100%, and the yellow the rest of the way to 100%. For &quot;Estimated Deaths,&quot; the blue section reaches from the bottom to about halfway between 20% and 30%, the orange from there to just over 50%, the gray from there to about one third of the way between 80% and 90%, and the yellow from there the rest of the way to 100%.\" width=\"1024\" height=\"817\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240991\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240991&theme=oea&iframe_resize_id=ohm240991\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q330314\">Hint<\/span><\/p>\n<div id=\"q330314\" class=\"hidden-answer\" style=\"display: none\">See the paragraph above the graph for guidance if needed.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240994\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240994&theme=oea&iframe_resize_id=ohm240994\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q282916\">Hint<\/span><\/p>\n<div id=\"q282916\" class=\"hidden-answer\" style=\"display: none\">See the paragraph above the graph for guidance if needed.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240996\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240996&theme=oea&iframe_resize_id=ohm240996\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q251689\">Hint<\/span><\/p>\n<div id=\"q251689\" class=\"hidden-answer\" style=\"display: none\">See the key for a description.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240794\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240794&theme=oea&iframe_resize_id=ohm240794\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q212822\">Hint<\/span><\/p>\n<div id=\"q212822\" class=\"hidden-answer\" style=\"display: none\">Remember that the total percentages of each segment add up to [latex]100[\/latex]%<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240795\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240795&theme=oea&iframe_resize_id=ohm240795\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q270540\">Hint<\/span><\/p>\n<div id=\"q270540\" class=\"hidden-answer\" style=\"display: none\">Remember that the total percentages of each segment add up to [latex]100[\/latex]%<\/div>\n<\/div>\n<\/div>\n<h3><strong>Changes in Percentages<\/strong><\/h3>\n<p>When examining data, it can sometimes be helpful to compare two values by taking their absolute change or their relative change.\u00a0It can be challenging, though, to compare relative change when data are presented as percentages. Before we try to understand how to apply these comparisons to percentages, please refresh your understanding of absolute and relative difference in the Recall box below.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>When computing absolute change and relative change between two values, we need one value that we think of as the starting point and the other that represents the value after some change. We&#8217;ll call the starting point value the\u00a0<strong>reference value<\/strong> and the second one will be the\u00a0<strong>new value<\/strong>. We&#8217;ll use these terms in the skill explanations below.<\/p>\n<p><span id=\"RecallAbs\">Core skill:<\/span><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q754599\">Compute absolute change between two values<\/span><\/p>\n<div id=\"q754599\" class=\"hidden-answer\" style=\"display: none\">\n<p>The\u00a0<strong>absolute change<\/strong> between two values indicates the actual increase or decrease from one value to the next.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\text{absolute change }=\\text{new value }-\\text{reference value}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Absolute change retains the units on the two values. For example a decrease in value from $[latex]15,000[\/latex] to $[latex]12,000[\/latex] is expressed in dollars.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]12,000\\text{ dollars } -15,000\\text{ dollars }=-3000\\text{ dollars }[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><em>The value decreased [latex]3,000[\/latex] dollars.\u00a0<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p><strong>When using percentage points as the unit, the absolute change is expressed in percentage points.<\/strong><\/p>\n<p>Ex. A survey indicates that [latex]50[\/latex]% of dentists polled would recommend a toothpaste. After the company improves the toothpaste, a new survey indicates that [latex]80[\/latex]% of dentists polled would recommend it.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]80\\text{ percentage points } -50\\text{ percentage points }=30\\text{ percentage points }[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><em>The number of dentists who recommend the toothpaste increased [latex]30[\/latex] percentage points.<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<\/div>\n<\/div>\n<p><span id=\"RecallRel\">Core skill:<\/span><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q434757\">Compute relative change between two values<\/span><\/p>\n<div id=\"q434757\" class=\"hidden-answer\" style=\"display: none\">\n<p>The\u00a0<strong>relative change<\/strong> between two values is a ratio that expresses the absolute change between two values relative to the reference value.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{\\text{absolute change}}{\\text{reference value}}=\\dfrac{\\text{new value }-\\text{reference value}}{\\text{reference value}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>The relative change in two values is unitless, since the units cancel from the numerator to the denominator.\u00a0We can express relative change as a percentage by multiplying by [latex]100[\/latex]%.<\/p>\n<p>&nbsp;<\/p>\n<p>Ex.\u00a0For example, the relative change in value from $[latex]15,000[\/latex] to $[latex]12,000[\/latex] is unitless, but may be expressed as a percentage.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(12,000-15,000\\right)\\text{ dollars }}{15,000\\text{ dollars }}=\\dfrac{-3,000 \\cancel{\\text{ dollars} }}{15,000\\cancel{\\text{ dollars} }}=-\\dfrac{1}{5}=-0.20\\times100\\%=-20\\%[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><em>The value decreased [latex]20[\/latex]%.\u00a0<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p><strong>When using percentage points as the unit, the relative change is unitless, but may be expressed as a percentage.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Ex. A survey indicated that [latex]50[\/latex]% of dentists polled would recommend a toothpaste. After the company improved the toothpaste, a new survey indicated that [latex]80[\/latex]% of dentists polled would recommend it.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(80-50\\right)\\text{ percentage points }}{50\\text{ percentage points }}=\\dfrac{30\\cancel{\\text{ percentage points} } }{50\\cancel{\\text{ percentage points} } }=\\dfrac{3}{5}=0.6\\times100\\%=60\\%[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em><strong>The number of dentists who would recommend the toothpaste increased [latex]60[\/latex]%.<\/strong><br \/>\n<\/em><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>It can be tricky to handle the units when they are in percentage points. Use this rule of thumb when\u00a0the original units are percentage points:<\/p>\n<ul>\n<li id=\"AbsPercent\">The <strong>absolute difference<\/strong> will be in percentage points, indicating the change occurred in a number of percentage points.<\/li>\n<li id=\"RelPercent\">The <strong>relative difference<\/strong> will be expressed with the [latex]\\%[\/latex] symbol, indicating that the amount of something has changed by some percent relative to its original amount.<\/li>\n<\/ul>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Consider a small town that suffered the downsizing of a large manufacturing plant. In 2010, [latex]60[\/latex]% of the town&#8217;s workers were employed in the plant. But in 2011, only [latex]27[\/latex]% of the town&#8217;s workers remained.<\/p>\n<p>What was the absolute change in the percentage of workers employed at the plant?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q583613\">Show Solution<\/span><\/p>\n<div id=\"q583613\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: center;\">[latex]27\\text{ percentage points } -60\\text{ percentage points }=-33\\text{ percentage points }[\/latex]<\/p>\n<p style=\"text-align: center;\"><strong><em>The number of workers from the town who worked at the plant decreased [latex]33[\/latex] percentage points.<\/em><\/strong><\/p>\n<\/div>\n<\/div>\n<p>What was the relative change?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q646464\">Show Solution<\/span><\/p>\n<p style=\"text-align: left;\">\n<div id=\"q646464\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: center;\">[latex]\\dfrac{\\left(27-60\\right)\\text{ percentage points }}{60\\text{ percentage points }}=\\dfrac{-33\\cancel{\\text{ percentage points} } }{60\\cancel{\\text{ percentage points} } }=-\\dfrac{11}{20}=-0.55\\times100\\%=-55\\%[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em><strong>The number of workers from the town who worked at the plant decreased [latex]55[\/latex]%.<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you try this scenario about graduation rates.<\/p>\n<p>In 2013, [latex]80[\/latex]% of the original class of 2013 (who started in 2009) graduated from Valley High School, and in 2014, [latex]73[\/latex]% of the original class of 2014 graduated.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240797\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240797&theme=oea&iframe_resize_id=ohm240797\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q818757\">Hint<\/span><\/p>\n<div id=\"q818757\" class=\"hidden-answer\" style=\"display: none\">Begin with the percentage from 2014.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240798\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240798&theme=oea&iframe_resize_id=ohm240798\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q220308\">Hint<\/span><\/p>\n<div id=\"q220308\" class=\"hidden-answer\" style=\"display: none\">See the recall box above for details.\u00a0 [latex]\\text{relative change }=\\dfrac{\\text{absolute change}}{\\text{reference value}}=\\dfrac{\\text{new value }-\\text{reference value}}{\\text{reference value}}\\times100\\%[\/latex], where the\u00a0<em>reference value<\/em> is the starting value.<span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><\/div>\n<\/div>\n<p><\/span><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240800\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240800&theme=oea&iframe_resize_id=ohm240800\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q55079\">Hint<\/span><\/p>\n<div id=\"q55079\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think? Have you been given any information about a number of students in either class?<\/div>\n<\/div>\n<\/div>\n<div>Now that you&#8217;ve gained some experience reading and interpreting graphs that represent percentages, it&#8217;s time to move on to the next section and activity.<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-231-1\"> Mateyka, P. J., Rapino, M. A., &amp; Landivar, L. C. (2012, October). Home-based workers in the United States: 2010. United States Census Bureau. https:\/\/www.census.gov\/prod\/2012pubs\/p70-132.pdf  <a href=\"#return-footnote-231-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-231-2\"> American Cancer Society. (2018). Table 1. Estimated number of new cancer cases and deaths by sex, US, 2018. https:\/\/www.cancer.org\/content\/dam\/cancer-org\/research\/cancer-facts-and-statistics\/annual-cancer-facts-and-figures\/2018\/estimated-number-of-new-cancer-cases-and-deaths-by-sex-us-2018.pdf.  <a href=\"#return-footnote-231-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":175116,"menu_order":8,"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-231","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/231","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/users\/175116"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/231\/revisions"}],"predecessor-version":[{"id":1193,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/231\/revisions\/1193"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/231\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=231"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=231"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=231"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=231"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}