{"id":330,"date":"2022-06-17T15:36:51","date_gmt":"2022-06-17T15:36:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/displaying-categorical-data-what-to-know\/"},"modified":"2022-06-17T16:51:26","modified_gmt":"2022-06-17T16:51:26","slug":"displaying-categorical-data-what-to-know","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/displaying-categorical-data-what-to-know\/","title":{"raw":"Displaying Categorical Data: What to Know 1","rendered":"Displaying Categorical Data: What to Know 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\n<ul>\r\n \t<li>Determine which variables are categorical from raw data.<\/li>\r\n \t<li>Read and interpret a frequency table<\/li>\r\n \t<li>Use a data analysis tool to create a frequency table from a dataset<\/li>\r\n \t<li>Read and interpret a bar graph.<\/li>\r\n \t<li>Use technology to create a bar graph from a dataset.<\/li>\r\n \t<li>Read and interpret a pie chart.<\/li>\r\n \t<li>Use technology to create a pie chart from a dataset.<\/li>\r\n<\/ul>\r\n<\/div>\r\nWhen describing data using graphical representations, certain variables in the data are appropriate for certain visualizations. To prepare for the upcoming activity, you will need to identify variables that would be appropriate for bar graphs and pie charts and answer research questions by reading bar graphs and pie charts. To do this, you will need to be able to determine which variables in a dataset are categorical, understand how frequency tables are formed, and understand how bar graphs and pie charts are formed.\r\n<h2>Categorical Variables<\/h2>\r\nIn Module 1,\u00a0<em>Data Collection and Organization<\/em>, you learned the difference between categorical and quantitative variables. Let's take a moment to refresh that information before diving into a deep exploration of categorical variables.\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nWhat is the distinguishing feature of a categorical variable? That is, how can we tell a categorical variable apart from a quantitative variable?\r\n<p style=\"text-align: left;\">Core Skill:[reveal-answer q=\"244835\"]Identify a variable as\u00a0categorical or quantitative[\/reveal-answer]<\/p>\r\n[hidden-answer a=\"244835\"]\r\n\r\nA variable is classified as <strong>categorical<\/strong> if it places an individual into one of several groups.\r\n<ul>\r\n \t<li>Eye color, zip code, education level, and gender are examples of categorical data.<\/li>\r\n<\/ul>\r\nA variable is classified as <strong>quantitative<\/strong> if it takes numerical values that can be manipulated arithmetically.\r\n<ul>\r\n \t<li>Height, cost, exam scores, and temperature are examples of quantitative data.<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nPractice identifying categorical variables in a list in the example. Then, for the data table that follows, identify the categorical variables to answer Question 1.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhich variable(s) in the list below are categorical?\r\n<p style=\"padding-left: 30px;\"><em>Age<\/em>, <em>marital status<\/em>, <em>number of children in the household<\/em>, <em>zip code<\/em>,<em> income<\/em>, <em>education level<\/em><\/p>\r\n[reveal-answer q=\"129517\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"129517\"]\r\n\r\nThe categorical variables are: <em>marital status<\/em>, <em>zip code<\/em>, <em>education level<\/em> since we cannot do arithmetic on these observations.\r\n\r\n<em>Age,\u00a0<\/em><em>Number of children in the household<\/em>, and\u00a0<em>income<\/em> are quantitative since we could find a numerical average of each of these.\r\n\r\nNote that <em>income<\/em> could be made categorical by collecting data in categories of income levels: under [latex]20[\/latex]k, [latex]21[\/latex]k-[latex]50[\/latex]k, [latex]51[\/latex]k-[latex]100[\/latex]k, etc.\u00a0[\/hidden-answer]\r\n\r\n<\/div>\r\nNow it's your turn to practice what you know by looking at a real dataset obtained from a survey and displayed in the table below. Read the information given about the dataset and its variables, then answer the questions that follow.\r\n<h3 id=\"Categorical Variables\">Variables in a dataset<\/h3>\r\n<div class=\"textbox tryit\">\r\n<h3>identifying characteristics of a categorical variable<\/h3>\r\n<strong><span style=\"background-color: #99cc00;\">[Perspective Video -- a 3-instructors video illustrating the identifying characteristics of a categorical variable in raw data.)<\/span><\/strong>\r\n\r\n<\/div>\r\nIn 2013, students of the statistics class at FSEV UK, a Slovakian University, were asked to invite their friends to participate in a survey[footnote]Young people survey. (2016, December 6). Kaggle. Retrieved from https:\/\/www.kaggle.com\/miroslavsabo\/young-people-survey[\/footnote]. Data for the first [latex]15[\/latex] out of [latex]1,007[\/latex] young people who completed the survey are displayed below.\r\n<table border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\" colspan=\"8\"><strong>Young People Survey<\/strong><strong>\r\n<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Alcohol<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Age<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Height<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Punctuality<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Number of siblings<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Enjoy Music 1=strongly disagree, 5=strongly agree<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Internet usage<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Left \u2013 right handed<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]163[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am always on time<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]163[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]4[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]176[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often running late<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]22[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]172[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">most of the day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]170[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am always on time<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">never<\/td>\r\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]186[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]177[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">less than an hour a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]184[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am always on time<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]18[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]166[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">drink a lot<\/td>\r\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]174[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often running late<\/td>\r\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]175[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">less than an hour a day<\/td>\r\n<td style=\"text-align: center;\">left handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">never<\/td>\r\n<td style=\"text-align: center;\">[latex]17[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]176[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often running late<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]24[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]168[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often running late<\/td>\r\n<td style=\"text-align: center;\">[latex]10[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]165[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">few hours a day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">social drinker<\/td>\r\n<td style=\"text-align: center;\">[latex]22[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]175[\/latex]<\/td>\r\n<td style=\"text-align: center;\">I am often early<\/td>\r\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center;\">most of the day<\/td>\r\n<td style=\"text-align: center;\">right handed<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe following eight variables are included in the dataset. The variable names are presented in <em>italics<\/em>, followed by a brief description. You may recall from Forming Connections in (1D) that this is often called a\u00a0<strong>data dictionary<\/strong>.\r\n<ul>\r\n \t<li><strong><em>Alcohol<\/em><\/strong>: \u201cnever,\u201d \u201csocial drinker,\u201d or \u201cdrink a lot\u201d<\/li>\r\n \t<li><strong><em>Age<\/em><\/strong>: Years<\/li>\r\n \t<li><strong><em>Height<\/em><\/strong>: Height in centimeters (cm)<\/li>\r\n \t<li><strong><em>Punctuality<\/em><\/strong>: \u201cI am often early,\u201d \u201cI am often on time,\u201d or \u201cI am often running late\u201d<\/li>\r\n \t<li><strong><em>Number of siblings <\/em><\/strong><\/li>\r\n \t<li><strong><em>Enjoy music<\/em><\/strong>: Participants were asked \u201cDo you enjoy music?\u201d and reported on a 5-point Likert scale: strongly disagree = 1, strongly agree = 5<\/li>\r\n \t<li><strong><em>Internet usage<\/em><\/strong>: \u201cno time at all,\u201d \u201cless than an hour a day,\u201d \u201cfew hours a day,\u201d or \u201cmost of the day\u201d<\/li>\r\n \t<li><strong><em>Left - right handed<\/em><\/strong><\/li>\r\n<\/ul>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240631[\/ohm_question]\r\n\r\n[reveal-answer q=\"576725\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"576725\"]Recall that a categorical variable is a variable that places an individual into one of several groups.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Frequency Tables<\/h2>\r\nA <strong>frequency table <\/strong>lists the number of observations (the <strong>frequency<\/strong>) of each unique value of a categorical variable. The frequency is commonly referred to as the <strong>count<\/strong>. See the example below, which illustrates a partially complete, simple frequency table for a survey in which [latex]20[\/latex] people were asked to answer a question by choosing one of four responses: strongly disagree, disagree, agree, or strongly agree.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n<table style=\"border-collapse: collapse; width: 44.444%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%; text-align: center;\">Variable Name<\/td>\r\n<td style=\"width: 33.3333%; text-align: center;\">Frequency (number of times each response appears in the dataset)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Strongly disagree<\/td>\r\n<td style=\"width: 33.3333%; text-align: center;\">[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Disagree<\/td>\r\n<td style=\"width: 33.3333%; text-align: center;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Agree<\/td>\r\n<td style=\"width: 33.3333%; text-align: center;\">[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Strongly agree<\/td>\r\n<td style=\"width: 33.3333%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFor the frequency table above, answer the following questions:\r\n\r\n<strong>a)<\/strong> If [latex]20[\/latex] responses were collected in the survey, how many people responded with \"Strongly agree?\"\r\n\r\n[reveal-answer q=\"596200\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"596200\"]There are [latex]4[\/latex] \"Strongly agree\" responses. I.e., if there are [latex]9[\/latex] + [latex]5[\/latex] + [latex]2[\/latex] = [latex]16[\/latex] responses showing, and if the total frequency is [latex]20[\/latex], then [latex]20[\/latex] - [latex]16[\/latex] = [latex]4[\/latex]. [\/hidden-answer]\r\n\r\n<strong>b)<\/strong> What is the total frequency for the table?\r\n\r\n[reveal-answer q=\"276251\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"276251\"] [latex]20[\/latex]. There were [latex]20[\/latex] total responses, which represents the total frequency.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3 id=\"Frequency Tables\">Interpreting frequency tables<\/h3>\r\nFrequency tables often include a column for the relative frequency. The <strong>relative frequency<\/strong> represents the proportion of observations that are in a particular category and can be expressed as a decimal or a percentage. To find relative frequency, divide the count of a particular category by the sum of all the counts. See the recall box below for a refresher on how to convert ratios to proportions and percentages. Also see the Student Resources: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\"><em>Fractions, Decimals, Percentages<\/em><\/a> and\u00a0<em><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Ratios+and+Fractions.pdf\">Ratios and Fractions<\/a>.<\/em>\r\n<div class=\"textbox examples\">\r\n<h3>Recall<\/h3>\r\nWhen calculating relative frequencies, you'll need to convert a proportion to a percent. You've probably done this before, so this should be a refresher.\r\n\r\nClick the link below to see how to convert the fraction [latex]\\dfrac{2}{15}[\/latex] to a proportion and then to a percentage.\r\n\r\nCore Skill: [reveal-answer q=\"177645\"]Convert a fraction to a decimal or a percent[\/reveal-answer]\r\n\r\n[hidden-answer a=\"177645\"]\r\n<ul>\r\n \t<li>To convert a ratio (a fraction) to a proportion in decimal form, divide the numerator by the denominator in a calculator. The result will be a number in decimal form.<\/li>\r\n \t<li>To convert the proportion from decimal form to a percentage, multiply it by [latex]100[\/latex]. That is, first locate the decimal point in the proportion, then move it two places to the right.<\/li>\r\n<\/ul>\r\nEx. In the table below, we see that [latex]\\dfrac{2}{15} = 0.1\\bar{3}[\/latex].\r\n\r\nTo convert [latex]0.1\\bar{3}[\/latex] to a percent, move the decimal two places to the right to obtain [latex]13.\\bar{3}[\/latex] (the bar over the [latex]3[\/latex] indicates that the [latex]3[\/latex] repeats without terminating). In the table below, the number is rounded to the hundredths place (two decimal places) as [latex]13.33[\/latex]%.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>creating a frequency table<\/h3>\r\n<strong><span style=\"background-color: #99cc00;\">[Worked Example -- a 3-instructors worked example of creating a frequency table for a categorical variable identified from a data table. )<\/span><\/strong>\r\n\r\n<\/div>\r\nThe following frequency table displays the frequency and relative frequency (as a decimal and a percentage) of the categorical variable <em>Alcohol <\/em>for the first [latex]15[\/latex] young people who responded to the survey.\r\n<table style=\"width: 437px; height: 80px;\">\r\n<tbody>\r\n<tr style=\"height: 20px;\">\r\n<td style=\"width: 82.75px; height: 20px; text-align: center;\"><strong>Alcohol <\/strong><\/td>\r\n<td style=\"width: 64.7344px; height: 20px; text-align: center;\"><strong>Frequency<\/strong><\/td>\r\n<td style=\"width: 146.844px; height: 20px; text-align: center;\"><strong>Relative Frequency<\/strong><\/td>\r\n<td style=\"width: 91.6719px; height: 20px; text-align: center;\"><strong>Percent\u00a0<\/strong><strong>(%)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 29px;\">\r\n<td style=\"width: 82.75px; height: 21px; text-align: center;\"><strong>Never<\/strong><\/td>\r\n<td style=\"width: 64.7344px; height: 21px; text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 146.844px; height: 21px; text-align: center;\">[latex]\\dfrac{2}{15} = 0.1333[\/latex]<\/td>\r\n<td style=\"width: 91.6719px; height: 21px; text-align: center;\">[latex]13.33[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 49px;\">\r\n<td style=\"width: 82.75px; height: 21px; text-align: center;\"><strong>Social drinker<\/strong><\/td>\r\n<td style=\"width: 64.7344px; height: 21px; text-align: center;\"><\/td>\r\n<td style=\"width: 146.844px; height: 21px; text-align: center;\"><\/td>\r\n<td style=\"width: 91.6719px; height: 21px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 10px;\">\r\n<td style=\"width: 82.75px; height: 18px; text-align: center;\"><strong>Drink a lot<\/strong><\/td>\r\n<td style=\"width: 64.7344px; height: 18px; text-align: center;\"><\/td>\r\n<td style=\"width: 146.844px; height: 18px; text-align: center;\"><\/td>\r\n<td style=\"width: 91.6719px; height: 18px; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240752[\/ohm_question]\r\n\r\n[reveal-answer q=\"849602\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"849602\"]To find the relative frequency, divide the frequency for each category by the total frequency. To find the percent column, you will convert the relative frequencies to percentages by multiplying by [latex]100[\/latex]. See Resource <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Rounding+and+Estimation.pdf\" target=\"_blank\" rel=\"noopener\"><strong>Rounding and Estimation<\/strong><\/a>, if needed.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<ul>\n<li>Determine which variables are categorical from raw data.<\/li>\n<li>Read and interpret a frequency table<\/li>\n<li>Use a data analysis tool to create a frequency table from a dataset<\/li>\n<li>Read and interpret a bar graph.<\/li>\n<li>Use technology to create a bar graph from a dataset.<\/li>\n<li>Read and interpret a pie chart.<\/li>\n<li>Use technology to create a pie chart from a dataset.<\/li>\n<\/ul>\n<\/div>\n<p>When describing data using graphical representations, certain variables in the data are appropriate for certain visualizations. To prepare for the upcoming activity, you will need to identify variables that would be appropriate for bar graphs and pie charts and answer research questions by reading bar graphs and pie charts. To do this, you will need to be able to determine which variables in a dataset are categorical, understand how frequency tables are formed, and understand how bar graphs and pie charts are formed.<\/p>\n<h2>Categorical Variables<\/h2>\n<p>In Module 1,\u00a0<em>Data Collection and Organization<\/em>, you learned the difference between categorical and quantitative variables. Let&#8217;s take a moment to refresh that information before diving into a deep exploration of categorical variables.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>What is the distinguishing feature of a categorical variable? That is, how can we tell a categorical variable apart from a quantitative variable?<\/p>\n<p style=\"text-align: left;\">Core Skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q244835\">Identify a variable as\u00a0categorical or quantitative<\/span><\/p>\n<div id=\"q244835\" class=\"hidden-answer\" style=\"display: none\">\n<p>A variable is classified as <strong>categorical<\/strong> if it places an individual into one of several groups.<\/p>\n<ul>\n<li>Eye color, zip code, education level, and gender are examples of categorical data.<\/li>\n<\/ul>\n<p>A variable is classified as <strong>quantitative<\/strong> if it takes numerical values that can be manipulated arithmetically.<\/p>\n<ul>\n<li>Height, cost, exam scores, and temperature are examples of quantitative data.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>Practice identifying categorical variables in a list in the example. Then, for the data table that follows, identify the categorical variables to answer Question 1.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Which variable(s) in the list below are categorical?<\/p>\n<p style=\"padding-left: 30px;\"><em>Age<\/em>, <em>marital status<\/em>, <em>number of children in the household<\/em>, <em>zip code<\/em>,<em> income<\/em>, <em>education level<\/em><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q129517\">Show Solution<\/span><\/p>\n<div id=\"q129517\" class=\"hidden-answer\" style=\"display: none\">\n<p>The categorical variables are: <em>marital status<\/em>, <em>zip code<\/em>, <em>education level<\/em> since we cannot do arithmetic on these observations.<\/p>\n<p><em>Age,\u00a0<\/em><em>Number of children in the household<\/em>, and\u00a0<em>income<\/em> are quantitative since we could find a numerical average of each of these.<\/p>\n<p>Note that <em>income<\/em> could be made categorical by collecting data in categories of income levels: under [latex]20[\/latex]k, [latex]21[\/latex]k-[latex]50[\/latex]k, [latex]51[\/latex]k-[latex]100[\/latex]k, etc.\u00a0<\/div>\n<\/div>\n<\/div>\n<p>Now it&#8217;s your turn to practice what you know by looking at a real dataset obtained from a survey and displayed in the table below. Read the information given about the dataset and its variables, then answer the questions that follow.<\/p>\n<h3 id=\"Categorical Variables\">Variables in a dataset<\/h3>\n<div class=\"textbox tryit\">\n<h3>identifying characteristics of a categorical variable<\/h3>\n<p><strong><span style=\"background-color: #99cc00;\">[Perspective Video &#8212; a 3-instructors video illustrating the identifying characteristics of a categorical variable in raw data.)<\/span><\/strong><\/p>\n<\/div>\n<p>In 2013, students of the statistics class at FSEV UK, a Slovakian University, were asked to invite their friends to participate in a survey<a class=\"footnote\" title=\"Young people survey. (2016, December 6). Kaggle. Retrieved from https:\/\/www.kaggle.com\/miroslavsabo\/young-people-survey\" id=\"return-footnote-330-1\" href=\"#footnote-330-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>. Data for the first [latex]15[\/latex] out of [latex]1,007[\/latex] young people who completed the survey are displayed below.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"8\"><strong>Young People Survey<\/strong><strong><br \/>\n<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Alcohol<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Age<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Height<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Punctuality<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Number of siblings<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Enjoy Music 1=strongly disagree, 5=strongly agree<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Internet usage<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Left \u2013 right handed<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]163[\/latex]<\/td>\n<td style=\"text-align: center;\">I am always on time<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]163[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]4[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]176[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often running late<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]22[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]172[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">most of the day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]170[\/latex]<\/td>\n<td style=\"text-align: center;\">I am always on time<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">never<\/td>\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]186[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]20[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]177[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">less than an hour a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]184[\/latex]<\/td>\n<td style=\"text-align: center;\">I am always on time<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]18[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]166[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">drink a lot<\/td>\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]174[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often running late<\/td>\n<td style=\"text-align: center;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]175[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">less than an hour a day<\/td>\n<td style=\"text-align: center;\">left handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">never<\/td>\n<td style=\"text-align: center;\">[latex]17[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]176[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often running late<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]24[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]168[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often running late<\/td>\n<td style=\"text-align: center;\">[latex]10[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]19[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]165[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">few hours a day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">social drinker<\/td>\n<td style=\"text-align: center;\">[latex]22[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]175[\/latex]<\/td>\n<td style=\"text-align: center;\">I am often early<\/td>\n<td style=\"text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center;\">most of the day<\/td>\n<td style=\"text-align: center;\">right handed<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The following eight variables are included in the dataset. The variable names are presented in <em>italics<\/em>, followed by a brief description. You may recall from Forming Connections in (1D) that this is often called a\u00a0<strong>data dictionary<\/strong>.<\/p>\n<ul>\n<li><strong><em>Alcohol<\/em><\/strong>: \u201cnever,\u201d \u201csocial drinker,\u201d or \u201cdrink a lot\u201d<\/li>\n<li><strong><em>Age<\/em><\/strong>: Years<\/li>\n<li><strong><em>Height<\/em><\/strong>: Height in centimeters (cm)<\/li>\n<li><strong><em>Punctuality<\/em><\/strong>: \u201cI am often early,\u201d \u201cI am often on time,\u201d or \u201cI am often running late\u201d<\/li>\n<li><strong><em>Number of siblings <\/em><\/strong><\/li>\n<li><strong><em>Enjoy music<\/em><\/strong>: Participants were asked \u201cDo you enjoy music?\u201d and reported on a 5-point Likert scale: strongly disagree = 1, strongly agree = 5<\/li>\n<li><strong><em>Internet usage<\/em><\/strong>: \u201cno time at all,\u201d \u201cless than an hour a day,\u201d \u201cfew hours a day,\u201d or \u201cmost of the day\u201d<\/li>\n<li><strong><em>Left &#8211; right handed<\/em><\/strong><\/li>\n<\/ul>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240631\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240631&theme=oea&iframe_resize_id=ohm240631\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q576725\">Hint<\/span><\/p>\n<div id=\"q576725\" class=\"hidden-answer\" style=\"display: none\">Recall that a categorical variable is a variable that places an individual into one of several groups.<\/div>\n<\/div>\n<\/div>\n<h2>Frequency Tables<\/h2>\n<p>A <strong>frequency table <\/strong>lists the number of observations (the <strong>frequency<\/strong>) of each unique value of a categorical variable. The frequency is commonly referred to as the <strong>count<\/strong>. See the example below, which illustrates a partially complete, simple frequency table for a survey in which [latex]20[\/latex] people were asked to answer a question by choosing one of four responses: strongly disagree, disagree, agree, or strongly agree.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<table style=\"border-collapse: collapse; width: 44.444%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%; text-align: center;\">Variable Name<\/td>\n<td style=\"width: 33.3333%; text-align: center;\">Frequency (number of times each response appears in the dataset)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Strongly disagree<\/td>\n<td style=\"width: 33.3333%; text-align: center;\">[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Disagree<\/td>\n<td style=\"width: 33.3333%; text-align: center;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Agree<\/td>\n<td style=\"width: 33.3333%; text-align: center;\">[latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Strongly agree<\/td>\n<td style=\"width: 33.3333%; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For the frequency table above, answer the following questions:<\/p>\n<p><strong>a)<\/strong> If [latex]20[\/latex] responses were collected in the survey, how many people responded with &#8220;Strongly agree?&#8221;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q596200\">Show Solution<\/span><\/p>\n<div id=\"q596200\" class=\"hidden-answer\" style=\"display: none\">There are [latex]4[\/latex] &#8220;Strongly agree&#8221; responses. I.e., if there are [latex]9[\/latex] + [latex]5[\/latex] + [latex]2[\/latex] = [latex]16[\/latex] responses showing, and if the total frequency is [latex]20[\/latex], then [latex]20[\/latex] &#8211; [latex]16[\/latex] = [latex]4[\/latex]. <\/div>\n<\/div>\n<p><strong>b)<\/strong> What is the total frequency for the table?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q276251\">Show Solution<\/span><\/p>\n<div id=\"q276251\" class=\"hidden-answer\" style=\"display: none\"> [latex]20[\/latex]. There were [latex]20[\/latex] total responses, which represents the total frequency.<\/div>\n<\/div>\n<\/div>\n<h3 id=\"Frequency Tables\">Interpreting frequency tables<\/h3>\n<p>Frequency tables often include a column for the relative frequency. The <strong>relative frequency<\/strong> represents the proportion of observations that are in a particular category and can be expressed as a decimal or a percentage. To find relative frequency, divide the count of a particular category by the sum of all the counts. See the recall box below for a refresher on how to convert ratios to proportions and percentages. Also see the Student Resources: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Fractions%2C+Decimals%2C+Percentages.pdf\"><em>Fractions, Decimals, Percentages<\/em><\/a> and\u00a0<em><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Ratios+and+Fractions.pdf\">Ratios and Fractions<\/a>.<\/em><\/p>\n<div class=\"textbox examples\">\n<h3>Recall<\/h3>\n<p>When calculating relative frequencies, you&#8217;ll need to convert a proportion to a percent. You&#8217;ve probably done this before, so this should be a refresher.<\/p>\n<p>Click the link below to see how to convert the fraction [latex]\\dfrac{2}{15}[\/latex] to a proportion and then to a percentage.<\/p>\n<p>Core Skill: <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q177645\">Convert a fraction to a decimal or a percent<\/span><\/p>\n<div id=\"q177645\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li>To convert a ratio (a fraction) to a proportion in decimal form, divide the numerator by the denominator in a calculator. The result will be a number in decimal form.<\/li>\n<li>To convert the proportion from decimal form to a percentage, multiply it by [latex]100[\/latex]. That is, first locate the decimal point in the proportion, then move it two places to the right.<\/li>\n<\/ul>\n<p>Ex. In the table below, we see that [latex]\\dfrac{2}{15} = 0.1\\bar{3}[\/latex].<\/p>\n<p>To convert [latex]0.1\\bar{3}[\/latex] to a percent, move the decimal two places to the right to obtain [latex]13.\\bar{3}[\/latex] (the bar over the [latex]3[\/latex] indicates that the [latex]3[\/latex] repeats without terminating). In the table below, the number is rounded to the hundredths place (two decimal places) as [latex]13.33[\/latex]%.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>creating a frequency table<\/h3>\n<p><strong><span style=\"background-color: #99cc00;\">[Worked Example &#8212; a 3-instructors worked example of creating a frequency table for a categorical variable identified from a data table. )<\/span><\/strong><\/p>\n<\/div>\n<p>The following frequency table displays the frequency and relative frequency (as a decimal and a percentage) of the categorical variable <em>Alcohol <\/em>for the first [latex]15[\/latex] young people who responded to the survey.<\/p>\n<table style=\"width: 437px; height: 80px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"width: 82.75px; height: 20px; text-align: center;\"><strong>Alcohol <\/strong><\/td>\n<td style=\"width: 64.7344px; height: 20px; text-align: center;\"><strong>Frequency<\/strong><\/td>\n<td style=\"width: 146.844px; height: 20px; text-align: center;\"><strong>Relative Frequency<\/strong><\/td>\n<td style=\"width: 91.6719px; height: 20px; text-align: center;\"><strong>Percent\u00a0<\/strong><strong>(%)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 29px;\">\n<td style=\"width: 82.75px; height: 21px; text-align: center;\"><strong>Never<\/strong><\/td>\n<td style=\"width: 64.7344px; height: 21px; text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 146.844px; height: 21px; text-align: center;\">[latex]\\dfrac{2}{15} = 0.1333[\/latex]<\/td>\n<td style=\"width: 91.6719px; height: 21px; text-align: center;\">[latex]13.33[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 49px;\">\n<td style=\"width: 82.75px; height: 21px; text-align: center;\"><strong>Social drinker<\/strong><\/td>\n<td style=\"width: 64.7344px; height: 21px; text-align: center;\"><\/td>\n<td style=\"width: 146.844px; height: 21px; text-align: center;\"><\/td>\n<td style=\"width: 91.6719px; height: 21px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 82.75px; height: 18px; text-align: center;\"><strong>Drink a lot<\/strong><\/td>\n<td style=\"width: 64.7344px; height: 18px; text-align: center;\"><\/td>\n<td style=\"width: 146.844px; height: 18px; text-align: center;\"><\/td>\n<td style=\"width: 91.6719px; height: 18px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240752\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240752&theme=oea&iframe_resize_id=ohm240752\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q849602\">Hint<\/span><\/p>\n<div id=\"q849602\" class=\"hidden-answer\" style=\"display: none\">To find the relative frequency, divide the frequency for each category by the total frequency. To find the percent column, you will convert the relative frequencies to percentages by multiplying by [latex]100[\/latex]. See Resource <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Stats+Exemplar\/Resource+-+Rounding+and+Estimation.pdf\" target=\"_blank\" rel=\"noopener\"><strong>Rounding and Estimation<\/strong><\/a>, if needed.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-330-1\">Young people survey. (2016, December 6). Kaggle. Retrieved from https:\/\/www.kaggle.com\/miroslavsabo\/young-people-survey <a href=\"#return-footnote-330-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":4,"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-330","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/330","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/330\/revisions"}],"predecessor-version":[{"id":399,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/330\/revisions\/399"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/160"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/330\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=330"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=330"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=330"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}