{"id":4040,"date":"2020-04-05T01:42:43","date_gmt":"2020-04-05T01:42:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4040"},"modified":"2021-02-06T00:00:20","modified_gmt":"2021-02-06T00:00:20","slug":"identifying-the-mode-of-a-set-of-numbers","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/identifying-the-mode-of-a-set-of-numbers\/","title":{"raw":"Identifying the Mode of a Set of Numbers","rendered":"Identifying the Mode of a Set of Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the mode of a set of numbers<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>The <em>average<\/em> is one number in a set of numbers that is somehow typical of the whole set of numbers. The mean and median are both often called the average. Yes, it can be confusing when the word average refers to two different numbers, the mean and the median! In fact, there is a third number that is also an average. This average is the mode. The mode of a set of numbers is the number that occurs the most. The frequency, is the number of times a number occurs. So the mode of a set of numbers is the number with the highest frequency.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Mode<\/h3>\r\nThe mode of a set of numbers is the number with the highest frequency.\r\n\r\n<\/div>\r\nSuppose Jolene kept track of the number of miles she ran since the start of the month, as shown in the calendar below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221818\/CNX_BMath_Figure_05_05_003_img.png\" alt=\"An image of a calendar is shown. On Thursday the first, labeled New Year's Day, is written 2 mi. On Saturday the third is written 15 mi. On the 4th, 8 mi. On the 6th, 3 mi. On the 7th, 8 mi. On the 9th, 5 mi. On the 10th, 8 mi.\" \/>\r\nIf we list the numbers in order it is easier to identify the one with the highest frequency.\r\n<p style=\"text-align: center\">[latex]2,3,5,8,8,8,15[\/latex]<\/p>\r\nJolene ran [latex]8[\/latex] miles three times, and every other distance is listed only once. So the mode of the data is [latex]8[\/latex] miles.\r\n<div class=\"textbox shaded\">\r\n<h3>Identify the mode of a set of numbers.<\/h3>\r\n<ol id=\"eip-id1168466097152\" class=\"stepwise\">\r\n \t<li>List the data values in numerical order.<\/li>\r\n \t<li>Count the number of times each value appears.<\/li>\r\n \t<li>The mode is the value with the highest frequency.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe ages of students in a college math class are listed below. Identify the mode.\r\n[latex]18,18,18,18,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,22,23,24,24,25,29,30,40,44[\/latex]\r\n\r\nSolution\r\nThe ages are already listed in order. We will make a table of frequencies to help identify the age with the highest frequency.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221820\/CNX_BMath_Figure_05_05_011_img.png\" alt=\"A table is shown with 2 rows. The first row is labeled 'Age' and lists the values: 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 40, and 44. The second row is labeled 'Frequency' and lists the values: 4, 3, 7, 2, 5, 1, 2, 1, 1, 1, 1, and 1.\" \/>\r\nNow look for the highest frequency. The highest frequency is [latex]7[\/latex], which corresponds to the age [latex]20[\/latex]. So the mode of the ages in this class is [latex]20[\/latex] years.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\nThe number of sick days employees used last year: [latex]3,6,2,3,7,5,6,2,4,2[\/latex]. Identify the mode.\r\n\r\n[reveal-answer q=\"602911\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"602911\"]\r\n\r\n[latex]2[\/latex][\/hidden-answer]\r\n\r\nThe number of handbags owned by women in a book club: [latex]5,6,3,1,5,8,1,5,8,5[\/latex]. Identify the mode.\r\n\r\n[reveal-answer q=\"589674\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"589674\"]\r\n\r\n[latex]5[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe data lists the heights (in inches) of students in a statistics class. Identify the mode.\r\n<table id=\"fs-id3456019\" class=\"unnumbered\" summary=\"A table is shown with eight columns and four rows. The numbers 56, 61, 63, 64, 65, 66, 67, 67, 60, 62, 63, 64, 65, 66, 67, 70, 60, 63, 63, 64, 66, 66, 67, 74, 61, 63, 64, 65. 66, 67, 67 are listed in individual cells.\">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>[latex]61[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]60[\/latex]<\/td>\r\n<td>[latex]62[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>[latex]70[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]60[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>[latex]74[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]61[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"165458\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"165458\"]\r\n\r\nSolution\r\nList each number with its frequency.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221822\/CNX_BMath_Figure_05_05_012_img.png\" alt=\"A table is shown with 2 rows. The first row is labeled \" \/>\r\nNow look for the highest frequency. The highest frequency is [latex]6[\/latex], which corresponds to the height [latex]67[\/latex] inches. So the mode of this set of heights is [latex]67[\/latex] inches.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\nThe ages of the students in a statistics class are listed here: [latex]19[\/latex] , [latex]20[\/latex] , [latex]23[\/latex] , [latex]23[\/latex] , [latex]38[\/latex] , [latex]21[\/latex] , [latex]19[\/latex] , [latex]21[\/latex] , [latex]19[\/latex] , [latex]21[\/latex] , [latex]20[\/latex] , [latex]43[\/latex] , [latex]20[\/latex] , [latex]23[\/latex] , [latex]17[\/latex] , [latex]21[\/latex] , [latex]21[\/latex] , [latex]20[\/latex] , [latex]29[\/latex] , [latex]18[\/latex] , [latex]28[\/latex] . What is the mode?\r\n\r\n[reveal-answer q=\"888357\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"888357\"]\r\n\r\n[latex]21[\/latex][\/hidden-answer]\r\n\r\nStudents listed the number of members in their household as follows: [latex]6[\/latex] , [latex]2[\/latex] , [latex]5[\/latex] , [latex]6[\/latex] , [latex]3[\/latex] , [latex]7[\/latex] , [latex]5[\/latex] , [latex]6[\/latex] , [latex]5[\/latex] , [latex]3[\/latex] , [latex]4[\/latex] , [latex]4[\/latex] , [latex]5[\/latex] , [latex]7[\/latex] , [latex]6[\/latex] , [latex]4[\/latex] , [latex]5[\/latex] , [latex]2[\/latex] , [latex]1[\/latex] , [latex]5[\/latex] . What is the mode?\r\n\r\n[reveal-answer q=\"888927\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"888927\"]\r\n\r\n[latex]5[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nSome data sets do not have a mode because no value appears more than any other. And some data sets have more than one mode. In a given set, if two or more data values have the same highest frequency, we say they are all modes.\r\n\r\nWatch the following video for another example of how to find the mode of a data set.\r\n\r\nhttps:\/\/youtu.be\/YhgXmO_FpHY","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the mode of a set of numbers<\/li>\n<\/ul>\n<\/div>\n<p>The <em>average<\/em> is one number in a set of numbers that is somehow typical of the whole set of numbers. The mean and median are both often called the average. Yes, it can be confusing when the word average refers to two different numbers, the mean and the median! In fact, there is a third number that is also an average. This average is the mode. The mode of a set of numbers is the number that occurs the most. The frequency, is the number of times a number occurs. So the mode of a set of numbers is the number with the highest frequency.<\/p>\n<div class=\"textbox shaded\">\n<h3>Mode<\/h3>\n<p>The mode of a set of numbers is the number with the highest frequency.<\/p>\n<\/div>\n<p>Suppose Jolene kept track of the number of miles she ran since the start of the month, as shown in the calendar below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221818\/CNX_BMath_Figure_05_05_003_img.png\" alt=\"An image of a calendar is shown. On Thursday the first, labeled New Year's Day, is written 2 mi. On Saturday the third is written 15 mi. On the 4th, 8 mi. On the 6th, 3 mi. On the 7th, 8 mi. On the 9th, 5 mi. On the 10th, 8 mi.\" \/><br \/>\nIf we list the numbers in order it is easier to identify the one with the highest frequency.<\/p>\n<p style=\"text-align: center\">[latex]2,3,5,8,8,8,15[\/latex]<\/p>\n<p>Jolene ran [latex]8[\/latex] miles three times, and every other distance is listed only once. So the mode of the data is [latex]8[\/latex] miles.<\/p>\n<div class=\"textbox shaded\">\n<h3>Identify the mode of a set of numbers.<\/h3>\n<ol id=\"eip-id1168466097152\" class=\"stepwise\">\n<li>List the data values in numerical order.<\/li>\n<li>Count the number of times each value appears.<\/li>\n<li>The mode is the value with the highest frequency.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The ages of students in a college math class are listed below. Identify the mode.<br \/>\n[latex]18,18,18,18,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,22,23,24,24,25,29,30,40,44[\/latex]<\/p>\n<p>Solution<br \/>\nThe ages are already listed in order. We will make a table of frequencies to help identify the age with the highest frequency.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221820\/CNX_BMath_Figure_05_05_011_img.png\" alt=\"A table is shown with 2 rows. The first row is labeled 'Age' and lists the values: 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 40, and 44. The second row is labeled 'Frequency' and lists the values: 4, 3, 7, 2, 5, 1, 2, 1, 1, 1, 1, and 1.\" \/><br \/>\nNow look for the highest frequency. The highest frequency is [latex]7[\/latex], which corresponds to the age [latex]20[\/latex]. So the mode of the ages in this class is [latex]20[\/latex] years.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p>The number of sick days employees used last year: [latex]3,6,2,3,7,5,6,2,4,2[\/latex]. Identify the mode.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q602911\">Show Solution<\/span><\/p>\n<div id=\"q602911\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]2[\/latex]<\/p><\/div>\n<\/div>\n<p>The number of handbags owned by women in a book club: [latex]5,6,3,1,5,8,1,5,8,5[\/latex]. Identify the mode.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q589674\">Show Solution<\/span><\/p>\n<div id=\"q589674\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]5[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The data lists the heights (in inches) of students in a statistics class. Identify the mode.<\/p>\n<table id=\"fs-id3456019\" class=\"unnumbered\" summary=\"A table is shown with eight columns and four rows. The numbers 56, 61, 63, 64, 65, 66, 67, 67, 60, 62, 63, 64, 65, 66, 67, 70, 60, 63, 63, 64, 66, 66, 67, 74, 61, 63, 64, 65. 66, 67, 67 are listed in individual cells.\">\n<tbody>\n<tr valign=\"top\">\n<td>[latex]56[\/latex]<\/td>\n<td>[latex]61[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>[latex]65[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]60[\/latex]<\/td>\n<td>[latex]62[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>[latex]65[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>[latex]70[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]60[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>[latex]74[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]61[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>[latex]65[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q165458\">Show Solution<\/span><\/p>\n<div id=\"q165458\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nList each number with its frequency.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221822\/CNX_BMath_Figure_05_05_012_img.png\" alt=\"A table is shown with 2 rows. The first row is labeled\" \/><br \/>\nNow look for the highest frequency. The highest frequency is [latex]6[\/latex], which corresponds to the height [latex]67[\/latex] inches. So the mode of this set of heights is [latex]67[\/latex] inches.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p>The ages of the students in a statistics class are listed here: [latex]19[\/latex] , [latex]20[\/latex] , [latex]23[\/latex] , [latex]23[\/latex] , [latex]38[\/latex] , [latex]21[\/latex] , [latex]19[\/latex] , [latex]21[\/latex] , [latex]19[\/latex] , [latex]21[\/latex] , [latex]20[\/latex] , [latex]43[\/latex] , [latex]20[\/latex] , [latex]23[\/latex] , [latex]17[\/latex] , [latex]21[\/latex] , [latex]21[\/latex] , [latex]20[\/latex] , [latex]29[\/latex] , [latex]18[\/latex] , [latex]28[\/latex] . What is the mode?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q888357\">Show Solution<\/span><\/p>\n<div id=\"q888357\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]21[\/latex]<\/p><\/div>\n<\/div>\n<p>Students listed the number of members in their household as follows: [latex]6[\/latex] , [latex]2[\/latex] , [latex]5[\/latex] , [latex]6[\/latex] , [latex]3[\/latex] , [latex]7[\/latex] , [latex]5[\/latex] , [latex]6[\/latex] , [latex]5[\/latex] , [latex]3[\/latex] , [latex]4[\/latex] , [latex]4[\/latex] , [latex]5[\/latex] , [latex]7[\/latex] , [latex]6[\/latex] , [latex]4[\/latex] , [latex]5[\/latex] , [latex]2[\/latex] , [latex]1[\/latex] , [latex]5[\/latex] . What is the mode?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q888927\">Show Solution<\/span><\/p>\n<div id=\"q888927\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]5[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>Some data sets do not have a mode because no value appears more than any other. And some data sets have more than one mode. In a given set, if two or more data values have the same highest frequency, we say they are all modes.<\/p>\n<p>Watch the following video for another example of how to find the mode of a data set.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Find the Mode of a Data Set\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/YhgXmO_FpHY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-4040\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Find the Mode of a Data Set. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/YhgXmO_FpHY\">https:\/\/youtu.be\/YhgXmO_FpHY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":25777,"menu_order":5,"template":"","meta":{"_candela_citation":"{\"0\":{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},\"1\":{\"type\":\"cc\",\"description\":\"Ex: Find the Mode of a Data Set\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/YhgXmO_FpHY\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},\"3\":{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen 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