{"id":340,"date":"2021-07-16T12:51:57","date_gmt":"2021-07-16T12:51:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=340"},"modified":"2023-12-05T08:40:51","modified_gmt":"2023-12-05T08:40:51","slug":"frequency-frequency-tables-and-levels-of-measurement-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/frequency-frequency-tables-and-levels-of-measurement-2\/","title":{"raw":"Frequency and Frequency Tables","rendered":"Frequency and Frequency Tables"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning OUTCOMES<\/h3>\r\n<ul id=\"objectives-list\">\r\n \t<li>Calculate and use relative frequencies and cumulative relative frequencies to answer questions about a distribution<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Converting Fractions to Decimals<\/h3>\r\nTo convert a fraction into a decimal, divide the numerator (the number above the division symbol) by the denominator (the number below the division symbol). In probability, the numerator represents the number of events, and the denominator represents the number of possible outcomes.\r\n\r\nExample: [latex]\\frac{3}{20} = 3 \\div 20 = 0.15[\/latex]\r\n\r\n<\/div>\r\n<h2 data-type=\"title\">Frequency<\/h2>\r\nTwenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: [latex]5[\/latex], [latex]6[\/latex], [latex]3[\/latex], [latex]3[\/latex], [latex]2[\/latex], [latex]4[\/latex], [latex]7[\/latex], [latex]5[\/latex], [latex]2[\/latex], [latex]3[\/latex], [latex]5[\/latex], [latex]6[\/latex], [latex]5[\/latex], [latex]4[\/latex], [latex]4[\/latex], [latex]3[\/latex], [latex]5[\/latex], [latex]2[\/latex], [latex]5[\/latex], [latex]3[\/latex].\r\n\r\nThe following table lists the different data values in ascending order and their frequencies.\r\n<table id=\"id10383738\" summary=\"This table presents the values provided in the previously given data set in the first column, and the frequency of each value in the second column.\"><caption><span data-type=\"title\">Frequency Table of Student Work Hours<\/span><\/caption>\r\n<thead>\r\n<tr>\r\n<th>DATA VALUE<\/th>\r\n<th>FREQUENCY<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nA <strong>frequency <\/strong>is the number of times a value of the data occurs. According to the table, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, [latex]20[\/latex], represents the total number of students included in the sample.\r\n\r\nA <strong>relative frequency<\/strong> is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample \u2014 in this case, [latex]20[\/latex]. Relative frequencies can be written as fractions, percents, or decimals.\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Calculating A Probability<\/h3>\r\nTo calculate the probability of an event occurring, you find the number of times the event occurs and divide that by the total number of possible outcomes.\r\n\r\n[latex]\\mathrm{Probability \\ of \\ an \\ event} = \\frac{\\mathrm{number \\ of \\ events}}{\\mathrm{number \\ of \\ outcomes}}[\/latex]\r\n\r\nExample: Rolling an odd number on a 6-sided die. There are 3 odd numbers (1, 3, 5) out of the 6 total numbers on the die.\r\n\r\n[latex]\\mathrm{Probability \\ of \\ rolling \\ an \\ odd \\ number} = \\frac{3}{6}[\/latex]\r\n\r\nNotice, the probability is not a simplified fraction, this is commonly seen in statistics how to find the probability of an event.\r\n\r\n<\/div>\r\n<table id=\"id10564303\" summary=\"Table shows data, frequency, and relative frequency.\"><caption>Frequency Table of Student Work Hours with Relative Frequencies<\/caption>\r\n<thead>\r\n<tr>\r\n<th>DATA VALUE<\/th>\r\n<th>FREQUENCY<\/th>\r\n<th>RELATIVE FREQUENCY<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{5}{20}[\/latex] or [latex]0.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{6}{20}[\/latex] or [latex]0.30[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{2}{20}[\/latex] or [latex]0.10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{1}{20}[\/latex] or [latex]0.05[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe sum of the values in the relative frequency column of the previous table is [latex]\\frac{20}{20}[\/latex], or [latex]1[\/latex].\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Converting Fractions to Decimals<\/h3>\r\nTo add fractions with like denominators, like the fractions we will have when calculating the relative frequency, you add the numerators and leave the denominators the same.\r\n\r\n<strong>Fraction Addition<\/strong>\r\n\r\nIf [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then\r\n\r\n[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]\r\nTo add fractions with a common denominators, add the numerators and place the sum over the common denominator.\r\n\r\nYou will be adding different numbers of events but the number of outcomes (denominator) in a situation does not change.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Adding or Subtracting Decimals<\/h3>\r\n<ol id=\"eip-id1168467213800\" class=\"stepwise\">\r\n \t<li>Write the numbers vertically so the decimal points line up.<\/li>\r\n \t<li>Use zeros as place holders, as needed.<\/li>\r\n \t<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<strong>Cumulative relative frequency<\/strong> is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in the table below.\r\n<table id=\"id10564302\" summary=\"Table shows data, frequency, relative frequency and cumulative relative frequency.\"><caption>Frequency Table of Student Work Hours with Relative and Cumulative Relative Frequencies<\/caption>\r\n<thead>\r\n<tr>\r\n<th>DATA VALUE<\/th>\r\n<th>FREQUENCY<\/th>\r\n<th><strong>RELATIVE <\/strong><strong>FREQUENCY<\/strong><\/th>\r\n<th><strong>CUMULATIVE RELATIVE FREQUENCY<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\r\n<td>[latex]0.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{5}{20}[\/latex] or [latex]0.25[\/latex]<\/td>\r\n<td>[latex]0.15 + 0.25 = 0.40[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\r\n<td>[latex]0.40 + 0.15 = 0.55[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{6}{20}[\/latex] or [latex]0.30[\/latex]<\/td>\r\n<td>[latex]0.55 + 0.30 = 0.85[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{2}{20}[\/latex] or [latex]0.10[\/latex]<\/td>\r\n<td>[latex]0.85 + 0.10 = 0.95[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]\\displaystyle\\frac{1}{20}[\/latex] or [latex]0.05[\/latex]<\/td>\r\n<td>[latex]0.95 + 0.05 = 1.00[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.\r\n<div class=\"textbox shaded\">\r\n<h3>NOTE<\/h3>\r\nBecause of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one.\r\n\r\n<\/div>\r\n<p data-type=\"title\"><strong>Table 1.12<\/strong> below\u00a0represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.<\/p>\r\n\r\n<table summary=\"Table 1.12 Frequency Table of Soccer Player Height \" data-id=\"id9703284\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">HEIGHTS<span data-type=\"newline\">\r\n<\/span>(INCHES)<\/th>\r\n<th scope=\"col\">FREQUENCY<\/th>\r\n<th scope=\"col\">RELATIVE<span data-type=\"newline\">\r\n<\/span>FREQUENCY<\/th>\r\n<th scope=\"col\">CUMULATIVE<span data-type=\"newline\">\r\n<\/span>RELATIVE<span data-type=\"newline\">\r\n<\/span>FREQUENCY<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">59.95\u201361.95<\/span><\/td>\r\n<td>5<\/td>\r\n<td>[latex]\\frac{5}{100} = 0.05 [\/latex]<\/td>\r\n<td>0.05<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">61.95\u201363.95<\/span><\/td>\r\n<td>3<\/td>\r\n<td>[latex]\\frac{3}{100}= 0.03[\/latex]<\/td>\r\n<td>0.05 + 0.03 = 0.08<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">63.95\u201365.95<\/span><\/td>\r\n<td>15<\/td>\r\n<td>[latex]\\frac{15}{100}= 0.15[\/latex]<\/td>\r\n<td>0.08 + 0.15 = 0.23<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">65.95\u201367.95<\/span><\/td>\r\n<td>40<\/td>\r\n<td>[latex]\\frac{40}{100} = 0.40[\/latex]<\/td>\r\n<td>0.23 + 0.40 = 0.63<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">67.95\u201369.95<\/span><\/td>\r\n<td>17<\/td>\r\n<td>[latex]\\frac{17}{100}= 0.17[\/latex]<\/td>\r\n<td>0.63 + 0.17 = 0.80<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">69.95\u201371.95<\/span><\/td>\r\n<td>12<\/td>\r\n<td>[latex]\\frac{12}{100}= 0.12[\/latex]<\/td>\r\n<td>0.80 + 0.12 = 0.92<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">71.95\u201373.95<\/span><\/td>\r\n<td>7<\/td>\r\n<td>[latex]\\frac{7}{100}= 0.07[\/latex]<\/td>\r\n<td>0.92 + 0.07 = 0.99<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">73.95\u201375.95<\/span><\/td>\r\n<td>1<\/td>\r\n<td>[latex]\\frac{1}{100}= 0.01[\/latex]<\/td>\r\n<td>0.99 + 0.01 = 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>Total = 100<\/strong><\/td>\r\n<td><strong>Total = 1.00<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>Table 1.12<\/strong>\r\n<p id=\"element-591\" class=\" \">The data in this table have been\u00a0grouped\u00a0into the following intervals:<\/p>\r\n\r\n<ul id=\"element-634\">\r\n \t<li>59.95 to 61.95 inches<\/li>\r\n \t<li>61.95 to 63.95 inches<\/li>\r\n \t<li>63.95 to 65.95 inches<\/li>\r\n \t<li>65.95 to 67.95 inches<\/li>\r\n \t<li>67.95 to 69.95 inches<\/li>\r\n \t<li>69.95 to 71.95 inches<\/li>\r\n \t<li>71.95 to 73.95 inches<\/li>\r\n \t<li>73.95 to 75.95 inches<\/li>\r\n<\/ul>\r\n<div class=\"textbox shaded\">\r\n<h3>NOTE<\/h3>\r\nThis example is used again in\u00a0Descriptive Statistics, where the method used to compute the intervals will be explained.\r\n\r\n<\/div>\r\nIn this sample, there are\u00a0<strong>5<\/strong>\u00a0players whose heights fall within the interval 59.95-61.95 inches,\u00a0<strong>3<\/strong>\u00a0players whose heights fall within the interval 61.95-63.95 inches,\u00a0<strong>15<\/strong>\u00a0players whose heights fall within the interval 63.95-65.95 inches,\u00a0<strong>40<\/strong>\u00a0players whose heights fall within the interval 65.95-67.95 inches,\u00a0<strong>17<\/strong>\u00a0players whose heights fall within the interval 67.95-69.95 inches,\u00a0<strong>12<\/strong>\u00a0players whose heights fall within the interval 69.95-71.95,\u00a0<strong>7<\/strong>\u00a0players whose heights fall within the interval 71.95-73.95, and\u00a0<strong>1<\/strong>\u00a0player whose heights fall within the interval 73.95-75.95. All heights fall between the endpoints of an interval and not at the endpoints.\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFrom Table 1.12, find the percentage of heights that are less than 65.95 inches.\r\n\r\n[reveal-answer q=\"561529\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"561529\"]If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then [latex]\\frac{23}{100}[\/latex] or 23%. This percentage is the cumulative relative frequency entry in the third row.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nTable 1.13\u00a0shows the amount, in inches, of annual rainfall in a sample of towns.\r\n<table style=\"height: 138px;\" summary=\"Table 1.13 \" data-id=\"fs-idm82680048\">\r\n<thead>\r\n<tr style=\"height: 12px;\">\r\n<th style=\"height: 12px; width: 128.719px;\" scope=\"col\">Rainfall (Inches)<\/th>\r\n<th style=\"height: 12px; width: 114.938px;\" scope=\"col\">Frequency<\/th>\r\n<th style=\"height: 12px; width: 227.266px;\" scope=\"col\">Relative Frequency<\/th>\r\n<th style=\"height: 12px; width: 170.938px;\" scope=\"col\">Cumulative Relative Frequency<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 128.719px;\">[latex]2.95\u20134.97[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 114.938px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 227.266px;\">[latex] \\frac{6}{50} = 0.12 [\/latex]<\/td>\r\n<td style=\"height: 12px; width: 170.938px;\">[latex]0.12[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 66px;\">\r\n<td style=\"height: 29px; width: 128.719px;\">[latex]4.97\u20136.99[\/latex]<\/td>\r\n<td style=\"height: 29px; width: 114.938px;\">[latex]7[\/latex]<\/td>\r\n<td style=\"height: 29px; width: 227.266px;\">[latex] \\frac{7}{50} = 0.14[\/latex]<\/td>\r\n<td style=\"height: 29px; width: 170.938px;\">[latex]0.12 + 0.14 = 0.26[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 66px;\">\r\n<td style=\"height: 27px; width: 128.719px;\">[latex]6.99\u20139.01[\/latex]<\/td>\r\n<td style=\"height: 27px; width: 114.938px;\">[latex]15[\/latex]<\/td>\r\n<td style=\"height: 27px; width: 227.266px;\">[latex] \\frac{15}{50} = 0.30[\/latex]<\/td>\r\n<td style=\"height: 27px; width: 170.938px;\">[latex]0.26 + 0.30 = 0.56[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 128.719px;\">[latex]9.01\u201311.03[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 114.938px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 227.266px;\">[latex] \\frac{8}{50} =0.16 [\/latex]<\/td>\r\n<td style=\"height: 12px; width: 170.938px;\">[latex]0.56 + 0.16 = 0.72[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 66px;\">\r\n<td style=\"height: 21px; width: 128.719px;\">[latex]11.03\u201313.05[\/latex]<\/td>\r\n<td style=\"height: 21px; width: 114.938px;\">[latex]9[\/latex]<\/td>\r\n<td style=\"height: 21px; width: 227.266px;\">[latex] \\frac{9}{50} = 0.18[\/latex]<\/td>\r\n<td style=\"height: 21px; width: 170.938px;\">[latex]0.72 + 0.18 = 0.90[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13px;\">\r\n<td style=\"height: 13px; width: 128.719px;\">[latex]13.05\u201315.07[\/latex]<\/td>\r\n<td style=\"height: 13px; width: 114.938px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"height: 13px; width: 227.266px;\"><span style=\"font-size: 1rem;\">[latex] \\frac{5}{50} = 0.10 [\/latex]<\/span><\/td>\r\n<td style=\"height: 13px; width: 170.938px;\">[latex]0.90 + 0.10 = 1.00[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 128.719px;\"><\/td>\r\n<td style=\"height: 12px; width: 114.938px;\">Total [latex]= 50[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 227.266px;\">Total\u00a0[latex]= 1.00[\/latex]<\/td>\r\n<td style=\"height: 12px; width: 170.938px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span><span class=\"os-number\">1.13<\/span><\/div>\r\n<div>From Table 1.13,\u00a0find the percentage of rainfall that is less than\u00a0[latex]9.01[\/latex] inches.<\/div>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFrom Table 1.12, find the percentage of heights that fall between 61.95 and 65.95 inches.\r\n\r\n[reveal-answer q=\"150488\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"150488\"]Add the relative frequencies in the second and third rows: [latex]0.03 + 0.15 = 0.18[\/latex] or [latex]18[\/latex]%.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFrom Table 1.13,\u00a0find the percentage of rainfall that is between [latex]6.99[\/latex] and [latex]13.05[\/latex] inches.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse the heights of the\u00a0[latex]100[\/latex] male semiprofessional soccer players in Table 1.12.\u00a0Fill in the blanks and check your answers.\r\n<ol id=\"element-162\" type=\"a\">\r\n \t<li>The percentage of heights that are from\u00a0[latex]67.95[\/latex] to [latex]71.95[\/latex] inches is: ____.<\/li>\r\n \t<li>The percentage of heights that are from\u00a0[latex]67.95[\/latex] to\u00a0[latex]73.95[\/latex] inches is: ____.<\/li>\r\n \t<li>The percentage of heights that are more than\u00a0[latex]65.95[\/latex] inches is: ____.<\/li>\r\n \t<li>The number of players in the sample who are between\u00a0[latex]61.95[\/latex] and\u00a0[latex]71.95[\/latex] inches tall is: ____.<\/li>\r\n \t<li>What kind of data are the heights?<\/li>\r\n \t<li>Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players.<\/li>\r\n<\/ol>\r\n<p id=\"element-683\" class=\" \">Remember, you\u00a0<strong>count frequencies<\/strong>. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.<\/p>\r\n[reveal-answer q=\"74896\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"74896\"]\r\n<ol>\r\n \t<li>[latex]29[\/latex]%<\/li>\r\n \t<li>[latex]36[\/latex]%<\/li>\r\n \t<li>[latex]77[\/latex]%<\/li>\r\n \t<li>[latex]87[\/latex]<\/li>\r\n \t<li>Quantitative continuous<\/li>\r\n \t<li>Get rosters from each team and choose a simple random sample from each<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFrom Table 1.13,\u00a0find the number of towns that have rainfall between [latex]2.95[\/latex] and [latex]9.01[\/latex] inches.\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\"><header>\r\n<h3 class=\"title\" data-type=\"title\">Activity<\/h3>\r\n<\/header>\r\n<p id=\"id8661133\" class=\" \">In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:<\/p>\r\n\r\n<ol id=\"element-889\">\r\n \t<li>What percentage of the students in your class have no siblings?<\/li>\r\n \t<li>What percentage of the students have from one to three siblings?<\/li>\r\n \t<li>What percentage of the students have fewer than three siblings?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nNineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:\u00a0<span id=\"set-element-392\" data-type=\"list\" data-list-type=\"labeled-item\" data-display=\"inline\"><span data-type=\"item\">2<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">7<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">3<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">2<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">18<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">15<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">20<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">7<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">18<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">12<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">13<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">12<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">4<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<\/span><\/span>. Table 1.14 was produced:\r\n<table summary=\"Table 1.14 Frequency of Commuting Distances \" data-id=\"id9833287\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">DATA<\/th>\r\n<th scope=\"col\">FREQUENCY<\/th>\r\n<th scope=\"col\">RELATIVE<span data-type=\"newline\">\r\n<\/span>FREQUENCY<\/th>\r\n<th scope=\"col\">CUMULATIVE<span data-type=\"newline\">\r\n<\/span>RELATIVE<span data-type=\"newline\">\r\n<\/span>FREQUENCY<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">3<\/span><\/td>\r\n<td>3<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{3}{19}[\/latex]<\/span><\/td>\r\n<td>0.1579<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">4<\/span><\/td>\r\n<td>1<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\r\n<td>0.2105<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">5<\/span><\/td>\r\n<td>3<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{3}{19}[\/latex]<\/span><\/td>\r\n<td>0.1579<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">7<\/span><\/td>\r\n<td>2<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{2}{19}[\/latex]<\/span><\/td>\r\n<td>0.2632<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">10<\/span><\/td>\r\n<td>3<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{4}{19}[\/latex]<\/span><\/td>\r\n<td>0.4737<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">12<\/span><\/td>\r\n<td>2<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{2}{19}[\/latex]<\/span><\/td>\r\n<td>0.7895<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">13<\/span><\/td>\r\n<td>1<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\r\n<td>0.8421<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">15<\/span><\/td>\r\n<td>1<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\r\n<td>0.8948<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">18<\/span><\/td>\r\n<td>1<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\r\n<td>0.9474<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">20<\/span><\/td>\r\n<td>1<\/td>\r\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\r\n<td>1.0000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTable 1.14 Frequency of Commuting Distances\r\n<ol id=\"element-582\" type=\"a\">\r\n \t<li>Is the table correct? If it is not correct, what is wrong?<\/li>\r\n \t<li>True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.<\/li>\r\n \t<li>What fraction of the people surveyed commute five or seven miles?<\/li>\r\n \t<li>What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"938118\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"938118\"]\r\n<ol id=\"solution-list-2\" type=\"a\">\r\n \t<li>No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.<\/li>\r\n \t<li>False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.<\/li>\r\n \t<li><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{5}{19}[\/latex]<\/span><\/li>\r\n \t<li><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{7}{19}, \\frac{12}{19}, \\frac{7}{19}[\/latex]<\/span><\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nTable 1.13\u00a0represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTable 1.15\u00a0contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.\r\n<table summary=\"Table 1.15 \" data-id=\"fs-idm52810848\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">Year<\/th>\r\n<th scope=\"col\">Total Number of Deaths<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>2000<\/td>\r\n<td>231<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2001<\/td>\r\n<td>21,357<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2002<\/td>\r\n<td>11,685<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2003<\/td>\r\n<td>33,819<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2004<\/td>\r\n<td>228,802<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2005<\/td>\r\n<td>88,003<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2006<\/td>\r\n<td>6,605<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2007<\/td>\r\n<td>712<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2008<\/td>\r\n<td>88,011<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2009<\/td>\r\n<td>1,790<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2010<\/td>\r\n<td>320,120<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2011<\/td>\r\n<td>21,953<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2012<\/td>\r\n<td>768<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total<\/td>\r\n<td>823,856<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTable 1.15\r\n<p id=\"fs-idm38990240\" class=\" \">Answer the following questions.<\/p>\r\n\r\n<ol id=\"fs-idm21722256\" type=\"a\">\r\n \t<li>What is the frequency of deaths measured from 2006 through 2009?<\/li>\r\n \t<li>What percentage of deaths occurred after 2009?<\/li>\r\n \t<li>What is the relative frequency of deaths that occurred in 2003 or earlier?<\/li>\r\n \t<li>What is the percentage of deaths that occurred in 2004?<\/li>\r\n \t<li>What kind of data are the numbers of deaths?<\/li>\r\n \t<li>The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"408570\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"408570\"]\r\n<ol id=\"fs-idm15442992\" type=\"a\">\r\n \t<li>97,118 (11.8%)<\/li>\r\n \t<li>41.6%<\/li>\r\n \t<li>[latex]\\frac{67,092}{823,356}[\/latex] or 0.081 or 8.1 %<\/li>\r\n \t<li>27.8%<\/li>\r\n \t<li>Quantitative discrete<\/li>\r\n \t<li>Quantitative continuous<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nTable 1.16\u00a0contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011.\r\n<table summary=\"Table 1.16 \" data-id=\"fs-idm74902768\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">Year<\/th>\r\n<th scope=\"col\">Total Number of Crashes<\/th>\r\n<th scope=\"col\">Year<\/th>\r\n<th scope=\"col\">Total Number of Crashes<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>1994<\/td>\r\n<td>36,254<\/td>\r\n<td>2004<\/td>\r\n<td>38,444<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1995<\/td>\r\n<td>37,241<\/td>\r\n<td>2005<\/td>\r\n<td>39,252<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1996<\/td>\r\n<td>37,494<\/td>\r\n<td>2006<\/td>\r\n<td>38,648<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1997<\/td>\r\n<td>37,324<\/td>\r\n<td>2007<\/td>\r\n<td>37,435<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1998<\/td>\r\n<td>37,107<\/td>\r\n<td>2008<\/td>\r\n<td>34,172<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1999<\/td>\r\n<td>37,140<\/td>\r\n<td>2009<\/td>\r\n<td>30,862<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2000<\/td>\r\n<td>37,526<\/td>\r\n<td>2010<\/td>\r\n<td>30,296<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2001<\/td>\r\n<td>37,862<\/td>\r\n<td>2011<\/td>\r\n<td>29,757<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2002<\/td>\r\n<td>38,491<\/td>\r\n<td>Total<\/td>\r\n<td>653,782<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2003<\/td>\r\n<td>38,477<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTable 1.16\r\n<p id=\"fs-idm72473616\" class=\" \">Answer the following questions.<\/p>\r\n\r\n<ol id=\"fs-idm94591440\" type=\"a\">\r\n \t<li>What is the frequency of deaths measured from 2000 through 2004?<\/li>\r\n \t<li>What percentage of deaths occurred after 2006?<\/li>\r\n \t<li>What is the relative frequency of deaths that occurred in 2000 or before?<\/li>\r\n \t<li>What is the percentage of deaths that occurred in 2011?<\/li>\r\n \t<li>What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning OUTCOMES<\/h3>\n<ul id=\"objectives-list\">\n<li>Calculate and use relative frequencies and cumulative relative frequencies to answer questions about a distribution<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall: Converting Fractions to Decimals<\/h3>\n<p>To convert a fraction into a decimal, divide the numerator (the number above the division symbol) by the denominator (the number below the division symbol). In probability, the numerator represents the number of events, and the denominator represents the number of possible outcomes.<\/p>\n<p>Example: [latex]\\frac{3}{20} = 3 \\div 20 = 0.15[\/latex]<\/p>\n<\/div>\n<h2 data-type=\"title\">Frequency<\/h2>\n<p>Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: [latex]5[\/latex], [latex]6[\/latex], [latex]3[\/latex], [latex]3[\/latex], [latex]2[\/latex], [latex]4[\/latex], [latex]7[\/latex], [latex]5[\/latex], [latex]2[\/latex], [latex]3[\/latex], [latex]5[\/latex], [latex]6[\/latex], [latex]5[\/latex], [latex]4[\/latex], [latex]4[\/latex], [latex]3[\/latex], [latex]5[\/latex], [latex]2[\/latex], [latex]5[\/latex], [latex]3[\/latex].<\/p>\n<p>The following table lists the different data values in ascending order and their frequencies.<\/p>\n<table id=\"id10383738\" summary=\"This table presents the values provided in the previously given data set in the first column, and the frequency of each value in the second column.\">\n<caption><span data-type=\"title\">Frequency Table of Student Work Hours<\/span><\/caption>\n<thead>\n<tr>\n<th>DATA VALUE<\/th>\n<th>FREQUENCY<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A <strong>frequency <\/strong>is the number of times a value of the data occurs. According to the table, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, [latex]20[\/latex], represents the total number of students included in the sample.<\/p>\n<p>A <strong>relative frequency<\/strong> is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample \u2014 in this case, [latex]20[\/latex]. Relative frequencies can be written as fractions, percents, or decimals.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall: Calculating A Probability<\/h3>\n<p>To calculate the probability of an event occurring, you find the number of times the event occurs and divide that by the total number of possible outcomes.<\/p>\n<p>[latex]\\mathrm{Probability \\ of \\ an \\ event} = \\frac{\\mathrm{number \\ of \\ events}}{\\mathrm{number \\ of \\ outcomes}}[\/latex]<\/p>\n<p>Example: Rolling an odd number on a 6-sided die. There are 3 odd numbers (1, 3, 5) out of the 6 total numbers on the die.<\/p>\n<p>[latex]\\mathrm{Probability \\ of \\ rolling \\ an \\ odd \\ number} = \\frac{3}{6}[\/latex]<\/p>\n<p>Notice, the probability is not a simplified fraction, this is commonly seen in statistics how to find the probability of an event.<\/p>\n<\/div>\n<table id=\"id10564303\" summary=\"Table shows data, frequency, and relative frequency.\">\n<caption>Frequency Table of Student Work Hours with Relative Frequencies<\/caption>\n<thead>\n<tr>\n<th>DATA VALUE<\/th>\n<th>FREQUENCY<\/th>\n<th>RELATIVE FREQUENCY<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{5}{20}[\/latex] or [latex]0.25[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{6}{20}[\/latex] or [latex]0.30[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{2}{20}[\/latex] or [latex]0.10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{1}{20}[\/latex] or [latex]0.05[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The sum of the values in the relative frequency column of the previous table is [latex]\\frac{20}{20}[\/latex], or [latex]1[\/latex].<\/p>\n<div class=\"textbox examples\">\n<h3>Recall: Converting Fractions to Decimals<\/h3>\n<p>To add fractions with like denominators, like the fractions we will have when calculating the relative frequency, you add the numerators and leave the denominators the same.<\/p>\n<p><strong>Fraction Addition<\/strong><\/p>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]<br \/>\nTo add fractions with a common denominators, add the numerators and place the sum over the common denominator.<\/p>\n<p>You will be adding different numbers of events but the number of outcomes (denominator) in a situation does not change.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall: Adding or Subtracting Decimals<\/h3>\n<ol id=\"eip-id1168467213800\" class=\"stepwise\">\n<li>Write the numbers vertically so the decimal points line up.<\/li>\n<li>Use zeros as place holders, as needed.<\/li>\n<li>Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.<\/li>\n<\/ol>\n<\/div>\n<p><strong>Cumulative relative frequency<\/strong> is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in the table below.<\/p>\n<table id=\"id10564302\" summary=\"Table shows data, frequency, relative frequency and cumulative relative frequency.\">\n<caption>Frequency Table of Student Work Hours with Relative and Cumulative Relative Frequencies<\/caption>\n<thead>\n<tr>\n<th>DATA VALUE<\/th>\n<th>FREQUENCY<\/th>\n<th><strong>RELATIVE <\/strong><strong>FREQUENCY<\/strong><\/th>\n<th><strong>CUMULATIVE RELATIVE FREQUENCY<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\n<td>[latex]0.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{5}{20}[\/latex] or [latex]0.25[\/latex]<\/td>\n<td>[latex]0.15 + 0.25 = 0.40[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{3}{20}[\/latex] or [latex]0.15[\/latex]<\/td>\n<td>[latex]0.40 + 0.15 = 0.55[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{6}{20}[\/latex] or [latex]0.30[\/latex]<\/td>\n<td>[latex]0.55 + 0.30 = 0.85[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{2}{20}[\/latex] or [latex]0.10[\/latex]<\/td>\n<td>[latex]0.85 + 0.10 = 0.95[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]\\displaystyle\\frac{1}{20}[\/latex] or [latex]0.05[\/latex]<\/td>\n<td>[latex]0.95 + 0.05 = 1.00[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.<\/p>\n<div class=\"textbox shaded\">\n<h3>NOTE<\/h3>\n<p>Because of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one.<\/p>\n<\/div>\n<p data-type=\"title\"><strong>Table 1.12<\/strong> below\u00a0represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.<\/p>\n<table summary=\"Table 1.12 Frequency Table of Soccer Player Height\" data-id=\"id9703284\">\n<thead>\n<tr>\n<th scope=\"col\">HEIGHTS<span data-type=\"newline\"><br \/>\n<\/span>(INCHES)<\/th>\n<th scope=\"col\">FREQUENCY<\/th>\n<th scope=\"col\">RELATIVE<span data-type=\"newline\"><br \/>\n<\/span>FREQUENCY<\/th>\n<th scope=\"col\">CUMULATIVE<span data-type=\"newline\"><br \/>\n<\/span>RELATIVE<span data-type=\"newline\"><br \/>\n<\/span>FREQUENCY<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">59.95\u201361.95<\/span><\/td>\n<td>5<\/td>\n<td>[latex]\\frac{5}{100} = 0.05[\/latex]<\/td>\n<td>0.05<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">61.95\u201363.95<\/span><\/td>\n<td>3<\/td>\n<td>[latex]\\frac{3}{100}= 0.03[\/latex]<\/td>\n<td>0.05 + 0.03 = 0.08<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">63.95\u201365.95<\/span><\/td>\n<td>15<\/td>\n<td>[latex]\\frac{15}{100}= 0.15[\/latex]<\/td>\n<td>0.08 + 0.15 = 0.23<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">65.95\u201367.95<\/span><\/td>\n<td>40<\/td>\n<td>[latex]\\frac{40}{100} = 0.40[\/latex]<\/td>\n<td>0.23 + 0.40 = 0.63<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">67.95\u201369.95<\/span><\/td>\n<td>17<\/td>\n<td>[latex]\\frac{17}{100}= 0.17[\/latex]<\/td>\n<td>0.63 + 0.17 = 0.80<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">69.95\u201371.95<\/span><\/td>\n<td>12<\/td>\n<td>[latex]\\frac{12}{100}= 0.12[\/latex]<\/td>\n<td>0.80 + 0.12 = 0.92<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">71.95\u201373.95<\/span><\/td>\n<td>7<\/td>\n<td>[latex]\\frac{7}{100}= 0.07[\/latex]<\/td>\n<td>0.92 + 0.07 = 0.99<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">73.95\u201375.95<\/span><\/td>\n<td>1<\/td>\n<td>[latex]\\frac{1}{100}= 0.01[\/latex]<\/td>\n<td>0.99 + 0.01 = 1.00<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong>Total = 100<\/strong><\/td>\n<td><strong>Total = 1.00<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Table 1.12<\/strong><\/p>\n<p id=\"element-591\" class=\"\">The data in this table have been\u00a0grouped\u00a0into the following intervals:<\/p>\n<ul id=\"element-634\">\n<li>59.95 to 61.95 inches<\/li>\n<li>61.95 to 63.95 inches<\/li>\n<li>63.95 to 65.95 inches<\/li>\n<li>65.95 to 67.95 inches<\/li>\n<li>67.95 to 69.95 inches<\/li>\n<li>69.95 to 71.95 inches<\/li>\n<li>71.95 to 73.95 inches<\/li>\n<li>73.95 to 75.95 inches<\/li>\n<\/ul>\n<div class=\"textbox shaded\">\n<h3>NOTE<\/h3>\n<p>This example is used again in\u00a0Descriptive Statistics, where the method used to compute the intervals will be explained.<\/p>\n<\/div>\n<p>In this sample, there are\u00a0<strong>5<\/strong>\u00a0players whose heights fall within the interval 59.95-61.95 inches,\u00a0<strong>3<\/strong>\u00a0players whose heights fall within the interval 61.95-63.95 inches,\u00a0<strong>15<\/strong>\u00a0players whose heights fall within the interval 63.95-65.95 inches,\u00a0<strong>40<\/strong>\u00a0players whose heights fall within the interval 65.95-67.95 inches,\u00a0<strong>17<\/strong>\u00a0players whose heights fall within the interval 67.95-69.95 inches,\u00a0<strong>12<\/strong>\u00a0players whose heights fall within the interval 69.95-71.95,\u00a0<strong>7<\/strong>\u00a0players whose heights fall within the interval 71.95-73.95, and\u00a0<strong>1<\/strong>\u00a0player whose heights fall within the interval 73.95-75.95. All heights fall between the endpoints of an interval and not at the endpoints.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>From Table 1.12, find the percentage of heights that are less than 65.95 inches.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q561529\">Show Answer<\/span><\/p>\n<div id=\"q561529\" class=\"hidden-answer\" style=\"display: none\">If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then [latex]\\frac{23}{100}[\/latex] or 23%. This percentage is the cumulative relative frequency entry in the third row.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Table 1.13\u00a0shows the amount, in inches, of annual rainfall in a sample of towns.<\/p>\n<table style=\"height: 138px;\" summary=\"Table 1.13\" data-id=\"fs-idm82680048\">\n<thead>\n<tr style=\"height: 12px;\">\n<th style=\"height: 12px; width: 128.719px;\" scope=\"col\">Rainfall (Inches)<\/th>\n<th style=\"height: 12px; width: 114.938px;\" scope=\"col\">Frequency<\/th>\n<th style=\"height: 12px; width: 227.266px;\" scope=\"col\">Relative Frequency<\/th>\n<th style=\"height: 12px; width: 170.938px;\" scope=\"col\">Cumulative Relative Frequency<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 128.719px;\">[latex]2.95\u20134.97[\/latex]<\/td>\n<td style=\"height: 12px; width: 114.938px;\">[latex]6[\/latex]<\/td>\n<td style=\"height: 12px; width: 227.266px;\">[latex]\\frac{6}{50} = 0.12[\/latex]<\/td>\n<td style=\"height: 12px; width: 170.938px;\">[latex]0.12[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 66px;\">\n<td style=\"height: 29px; width: 128.719px;\">[latex]4.97\u20136.99[\/latex]<\/td>\n<td style=\"height: 29px; width: 114.938px;\">[latex]7[\/latex]<\/td>\n<td style=\"height: 29px; width: 227.266px;\">[latex]\\frac{7}{50} = 0.14[\/latex]<\/td>\n<td style=\"height: 29px; width: 170.938px;\">[latex]0.12 + 0.14 = 0.26[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 66px;\">\n<td style=\"height: 27px; width: 128.719px;\">[latex]6.99\u20139.01[\/latex]<\/td>\n<td style=\"height: 27px; width: 114.938px;\">[latex]15[\/latex]<\/td>\n<td style=\"height: 27px; width: 227.266px;\">[latex]\\frac{15}{50} = 0.30[\/latex]<\/td>\n<td style=\"height: 27px; width: 170.938px;\">[latex]0.26 + 0.30 = 0.56[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 128.719px;\">[latex]9.01\u201311.03[\/latex]<\/td>\n<td style=\"height: 12px; width: 114.938px;\">[latex]8[\/latex]<\/td>\n<td style=\"height: 12px; width: 227.266px;\">[latex]\\frac{8}{50} =0.16[\/latex]<\/td>\n<td style=\"height: 12px; width: 170.938px;\">[latex]0.56 + 0.16 = 0.72[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 66px;\">\n<td style=\"height: 21px; width: 128.719px;\">[latex]11.03\u201313.05[\/latex]<\/td>\n<td style=\"height: 21px; width: 114.938px;\">[latex]9[\/latex]<\/td>\n<td style=\"height: 21px; width: 227.266px;\">[latex]\\frac{9}{50} = 0.18[\/latex]<\/td>\n<td style=\"height: 21px; width: 170.938px;\">[latex]0.72 + 0.18 = 0.90[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 13px;\">\n<td style=\"height: 13px; width: 128.719px;\">[latex]13.05\u201315.07[\/latex]<\/td>\n<td style=\"height: 13px; width: 114.938px;\">[latex]5[\/latex]<\/td>\n<td style=\"height: 13px; width: 227.266px;\"><span style=\"font-size: 1rem;\">[latex]\\frac{5}{50} = 0.10[\/latex]<\/span><\/td>\n<td style=\"height: 13px; width: 170.938px;\">[latex]0.90 + 0.10 = 1.00[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 128.719px;\"><\/td>\n<td style=\"height: 12px; width: 114.938px;\">Total [latex]= 50[\/latex]<\/td>\n<td style=\"height: 12px; width: 227.266px;\">Total\u00a0[latex]= 1.00[\/latex]<\/td>\n<td style=\"height: 12px; width: 170.938px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span><span class=\"os-number\">1.13<\/span><\/div>\n<div>From Table 1.13,\u00a0find the percentage of rainfall that is less than\u00a0[latex]9.01[\/latex] inches.<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>From Table 1.12, find the percentage of heights that fall between 61.95 and 65.95 inches.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q150488\">Show Answer<\/span><\/p>\n<div id=\"q150488\" class=\"hidden-answer\" style=\"display: none\">Add the relative frequencies in the second and third rows: [latex]0.03 + 0.15 = 0.18[\/latex] or [latex]18[\/latex]%.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>From Table 1.13,\u00a0find the percentage of rainfall that is between [latex]6.99[\/latex] and [latex]13.05[\/latex] inches.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use the heights of the\u00a0[latex]100[\/latex] male semiprofessional soccer players in Table 1.12.\u00a0Fill in the blanks and check your answers.<\/p>\n<ol id=\"element-162\" type=\"a\">\n<li>The percentage of heights that are from\u00a0[latex]67.95[\/latex] to [latex]71.95[\/latex] inches is: ____.<\/li>\n<li>The percentage of heights that are from\u00a0[latex]67.95[\/latex] to\u00a0[latex]73.95[\/latex] inches is: ____.<\/li>\n<li>The percentage of heights that are more than\u00a0[latex]65.95[\/latex] inches is: ____.<\/li>\n<li>The number of players in the sample who are between\u00a0[latex]61.95[\/latex] and\u00a0[latex]71.95[\/latex] inches tall is: ____.<\/li>\n<li>What kind of data are the heights?<\/li>\n<li>Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players.<\/li>\n<\/ol>\n<p id=\"element-683\" class=\"\">Remember, you\u00a0<strong>count frequencies<\/strong>. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q74896\">Show Answer<\/span><\/p>\n<div id=\"q74896\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]29[\/latex]%<\/li>\n<li>[latex]36[\/latex]%<\/li>\n<li>[latex]77[\/latex]%<\/li>\n<li>[latex]87[\/latex]<\/li>\n<li>Quantitative continuous<\/li>\n<li>Get rosters from each team and choose a simple random sample from each<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>From Table 1.13,\u00a0find the number of towns that have rainfall between [latex]2.95[\/latex] and [latex]9.01[\/latex] inches.<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<header>\n<h3 class=\"title\" data-type=\"title\">Activity<\/h3>\n<\/header>\n<p id=\"id8661133\" class=\"\">In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:<\/p>\n<ol id=\"element-889\">\n<li>What percentage of the students in your class have no siblings?<\/li>\n<li>What percentage of the students have from one to three siblings?<\/li>\n<li>What percentage of the students have fewer than three siblings?<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:\u00a0<span id=\"set-element-392\" data-type=\"list\" data-list-type=\"labeled-item\" data-display=\"inline\"><span data-type=\"item\">2<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">7<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">3<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">2<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">18<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">15<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">20<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">7<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">18<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">12<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">13<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">12<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">4<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">5<span class=\"-os-inline-list-separator\">;\u00a0<\/span><\/span><span data-type=\"item\">10<\/span><\/span>. Table 1.14 was produced:<\/p>\n<table summary=\"Table 1.14 Frequency of Commuting Distances\" data-id=\"id9833287\">\n<thead>\n<tr>\n<th scope=\"col\">DATA<\/th>\n<th scope=\"col\">FREQUENCY<\/th>\n<th scope=\"col\">RELATIVE<span data-type=\"newline\"><br \/>\n<\/span>FREQUENCY<\/th>\n<th scope=\"col\">CUMULATIVE<span data-type=\"newline\"><br \/>\n<\/span>RELATIVE<span data-type=\"newline\"><br \/>\n<\/span>FREQUENCY<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">3<\/span><\/td>\n<td>3<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{3}{19}[\/latex]<\/span><\/td>\n<td>0.1579<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">4<\/span><\/td>\n<td>1<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\n<td>0.2105<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">5<\/span><\/td>\n<td>3<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{3}{19}[\/latex]<\/span><\/td>\n<td>0.1579<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">7<\/span><\/td>\n<td>2<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{2}{19}[\/latex]<\/span><\/td>\n<td>0.2632<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">10<\/span><\/td>\n<td>3<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{4}{19}[\/latex]<\/span><\/td>\n<td>0.4737<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">12<\/span><\/td>\n<td>2<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{2}{19}[\/latex]<\/span><\/td>\n<td>0.7895<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">13<\/span><\/td>\n<td>1<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\n<td>0.8421<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">15<\/span><\/td>\n<td>1<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\n<td>0.8948<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">18<\/span><\/td>\n<td>1<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\n<td>0.9474<\/td>\n<\/tr>\n<tr>\n<td><span class=\"normal\" data-type=\"emphasis\" data-effect=\"normal\">20<\/span><\/td>\n<td>1<\/td>\n<td><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{1}{19}[\/latex]<\/span><\/td>\n<td>1.0000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Table 1.14 Frequency of Commuting Distances<\/p>\n<ol id=\"element-582\" type=\"a\">\n<li>Is the table correct? If it is not correct, what is wrong?<\/li>\n<li>True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.<\/li>\n<li>What fraction of the people surveyed commute five or seven miles?<\/li>\n<li>What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q938118\">Show Answer<\/span><\/p>\n<div id=\"q938118\" class=\"hidden-answer\" style=\"display: none\">\n<ol id=\"solution-list-2\" type=\"a\">\n<li>No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.<\/li>\n<li>False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.<\/li>\n<li><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{5}{19}[\/latex]<\/span><\/li>\n<li><span style=\"font-size: 14px; white-space: nowrap;\">[latex]\\frac{7}{19}, \\frac{12}{19}, \\frac{7}{19}[\/latex]<\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Table 1.13\u00a0represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Table 1.15\u00a0contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.<\/p>\n<table summary=\"Table 1.15\" data-id=\"fs-idm52810848\">\n<thead>\n<tr>\n<th scope=\"col\">Year<\/th>\n<th scope=\"col\">Total Number of Deaths<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>2000<\/td>\n<td>231<\/td>\n<\/tr>\n<tr>\n<td>2001<\/td>\n<td>21,357<\/td>\n<\/tr>\n<tr>\n<td>2002<\/td>\n<td>11,685<\/td>\n<\/tr>\n<tr>\n<td>2003<\/td>\n<td>33,819<\/td>\n<\/tr>\n<tr>\n<td>2004<\/td>\n<td>228,802<\/td>\n<\/tr>\n<tr>\n<td>2005<\/td>\n<td>88,003<\/td>\n<\/tr>\n<tr>\n<td>2006<\/td>\n<td>6,605<\/td>\n<\/tr>\n<tr>\n<td>2007<\/td>\n<td>712<\/td>\n<\/tr>\n<tr>\n<td>2008<\/td>\n<td>88,011<\/td>\n<\/tr>\n<tr>\n<td>2009<\/td>\n<td>1,790<\/td>\n<\/tr>\n<tr>\n<td>2010<\/td>\n<td>320,120<\/td>\n<\/tr>\n<tr>\n<td>2011<\/td>\n<td>21,953<\/td>\n<\/tr>\n<tr>\n<td>2012<\/td>\n<td>768<\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td>823,856<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Table 1.15<\/p>\n<p id=\"fs-idm38990240\" class=\"\">Answer the following questions.<\/p>\n<ol id=\"fs-idm21722256\" type=\"a\">\n<li>What is the frequency of deaths measured from 2006 through 2009?<\/li>\n<li>What percentage of deaths occurred after 2009?<\/li>\n<li>What is the relative frequency of deaths that occurred in 2003 or earlier?<\/li>\n<li>What is the percentage of deaths that occurred in 2004?<\/li>\n<li>What kind of data are the numbers of deaths?<\/li>\n<li>The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q408570\">Show Answer<\/span><\/p>\n<div id=\"q408570\" class=\"hidden-answer\" style=\"display: none\">\n<ol id=\"fs-idm15442992\" type=\"a\">\n<li>97,118 (11.8%)<\/li>\n<li>41.6%<\/li>\n<li>[latex]\\frac{67,092}{823,356}[\/latex] or 0.081 or 8.1 %<\/li>\n<li>27.8%<\/li>\n<li>Quantitative discrete<\/li>\n<li>Quantitative continuous<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Table 1.16\u00a0contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011.<\/p>\n<table summary=\"Table 1.16\" data-id=\"fs-idm74902768\">\n<thead>\n<tr>\n<th scope=\"col\">Year<\/th>\n<th scope=\"col\">Total Number of Crashes<\/th>\n<th scope=\"col\">Year<\/th>\n<th scope=\"col\">Total Number of Crashes<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1994<\/td>\n<td>36,254<\/td>\n<td>2004<\/td>\n<td>38,444<\/td>\n<\/tr>\n<tr>\n<td>1995<\/td>\n<td>37,241<\/td>\n<td>2005<\/td>\n<td>39,252<\/td>\n<\/tr>\n<tr>\n<td>1996<\/td>\n<td>37,494<\/td>\n<td>2006<\/td>\n<td>38,648<\/td>\n<\/tr>\n<tr>\n<td>1997<\/td>\n<td>37,324<\/td>\n<td>2007<\/td>\n<td>37,435<\/td>\n<\/tr>\n<tr>\n<td>1998<\/td>\n<td>37,107<\/td>\n<td>2008<\/td>\n<td>34,172<\/td>\n<\/tr>\n<tr>\n<td>1999<\/td>\n<td>37,140<\/td>\n<td>2009<\/td>\n<td>30,862<\/td>\n<\/tr>\n<tr>\n<td>2000<\/td>\n<td>37,526<\/td>\n<td>2010<\/td>\n<td>30,296<\/td>\n<\/tr>\n<tr>\n<td>2001<\/td>\n<td>37,862<\/td>\n<td>2011<\/td>\n<td>29,757<\/td>\n<\/tr>\n<tr>\n<td>2002<\/td>\n<td>38,491<\/td>\n<td>Total<\/td>\n<td>653,782<\/td>\n<\/tr>\n<tr>\n<td>2003<\/td>\n<td>38,477<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Table 1.16<\/p>\n<p id=\"fs-idm72473616\" class=\"\">Answer the following questions.<\/p>\n<ol id=\"fs-idm94591440\" type=\"a\">\n<li>What is the frequency of deaths measured from 2000 through 2004?<\/li>\n<li>What percentage of deaths occurred after 2006?<\/li>\n<li>What is the relative frequency of deaths that occurred in 2000 or before?<\/li>\n<li>What is the percentage of deaths that occurred in 2011?<\/li>\n<li>What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.<\/li>\n<\/ol>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-340\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Frequency, Frequency Tables, and Levels of Measurement. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-3-frequency-frequency-tables-and-levels-of-measurement\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-3-frequency-frequency-tables-and-levels-of-measurement<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><li>Prealgebra. <strong>Authored by<\/strong>: Lynn Marecek, MaryAnne Anthony-Smith. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\">https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Frequency, Frequency Tables, and Levels of Measurement\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-3-frequency-frequency-tables-and-levels-of-measurement\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"Lynn Marecek, MaryAnne Anthony-Smith\",\"organization\":\"Open Stax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at 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