{"id":413,"date":"2016-10-12T18:23:03","date_gmt":"2016-10-12T18:23:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/math4libarts\/?post_type=chapter&#038;p=413"},"modified":"2026-02-09T02:32:56","modified_gmt":"2026-02-09T02:32:56","slug":"4-10-presenting-quantitative-data-graphically","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/4-10-presenting-quantitative-data-graphically\/","title":{"raw":"4.10 Presenting Quantitative Data Graphically","rendered":"4.10 Presenting Quantitative Data Graphically"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Create a histogram that represents a data set<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Visualizing Numbers<\/h2>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/22162428\/numbers-738068_1280.jpg\"><img class=\"aligncenter size-large wp-image-952\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/22162428\/numbers-738068_1280-1024x576.jpg\" alt=\"Blue background with magnetic numbers attached to it. 1-5 are arranged sequentially at the top, while remaining digits are clustered at the bottom right\" width=\"1024\" height=\"576\" \/><\/a>\r\n\r\nQuantitative, or numerical, data can also be summarized into frequency tables.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nThe exam scores from 75 students were sorted from lowest to highest.\r\n\r\n32, 32, 33, 34, 38, 40, 41, 43, 44, 44, 45, 46, 47, 48, 48, 53, 53, 53, 54, 55, 55, 58, 59, 59, 59, 60, 60, 60, 64, 64, 64, 64, 65, 65, 65, 67, 67, 67, 67, 67, 68, 68, 68, 69, 69, 71, 72, 72, 72, 74, 74, 75, 75, 75, 77, 77, 78, 78, 79, 79, 80, 80, 80, 81, 83, 83, 84, 85, 86, 86, 90, 90, 91, 94, 97\r\n\r\nA <strong>frequency table<\/strong> can be created by grouping the scores in the following intervals: 30 \u2013 39, 40 \u2013 49, 50 \u2013 59, 60 \u2013 69, 70 \u2013 79, 80 \u2013 89, 90 \u2013 99.\r\n<p style=\"text-align: center;\"><strong>Frequency Table of Exam Scores<\/strong><\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">Intervals of Scores<\/td>\r\n<td style=\"width: 50%; height: 12px;\">Frequency (or Count of Students Earning Scores in this Interval)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">30 \u2013 39<\/td>\r\n<td style=\"width: 50%; height: 12px;\">5<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">40 \u2013 49<\/td>\r\n<td style=\"width: 50%; height: 12px;\">10<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">50 \u2013 59<\/td>\r\n<td style=\"width: 50%; height: 12px;\">10<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">60 \u2013 69<\/td>\r\n<td style=\"width: 50%; height: 12px;\">20<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">70 \u2013 79<\/td>\r\n<td style=\"width: 50%; height: 12px;\">15<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 50%; height: 12px;\">80 \u2013 89<\/td>\r\n<td style=\"width: 50%; height: 12px;\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">90 \u2013 99<\/td>\r\n<td style=\"width: 50%;\">5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nA graph can be created from the frequency table. This type of graph is called a <strong>histogram<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29224548\/Histogram.jpg\"><img class=\"wp-image-6743 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29224548\/Histogram-300x187.jpg\" alt=\"\" width=\"693\" height=\"432\" \/><\/a>\r\n\r\n<\/div>\r\n<div><\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>DIFFERENCE BETWEEN BAR GRAPHS AND HISTOGRAMS<\/h3>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29230843\/Bar-v-Histo.jpg\"><img class=\"wp-image-6747 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29230843\/Bar-v-Histo.jpg\" alt=\"\" width=\"791\" height=\"496\" \/><\/a>\r\n\r\nHistograms are different from bar graphs. The horizontal axis in a bar graph has categories. The horizontal axis in a histogram is a continuous number line. In addition, the bars in a bar graph do not touch, but the bars (also called <strong>classes<\/strong>) in histogram do touch.\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n\r\n<strong>HISTOGRAM<\/strong>\r\n\r\nA histogram is a graph where the horizontal axis is a continuous number line. Data are grouped into equally spaced intervals. The intervals are called <strong>classes<\/strong>. Rectangles are drawn to represent the classes. The height of the rectangle can either be the frequency (or count of the number of data points in each class) or it can be the <strong>relative frequency<\/strong> (the frequency divided by the total count).\r\n\r\n<\/div>\r\nUnfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.\r\n\r\nIf we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into <strong>class intervals<\/strong>.\r\n<div class=\"textbox\">\r\n<h3>Class Intervals<\/h3>\r\nClass intervals are groupings of the data. In general, we define class intervals so that\r\n<ul>\r\n \t<li>each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.<\/li>\r\n \t<li>we have somewhere between 5 and 20 classes, typically, depending upon the number of data we\u2019re working with.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSuppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Oftentimes we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Interval<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>120 - 134<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>135 \u2013 149<\/td>\r\n<td>14<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>150 \u2013 164<\/td>\r\n<td>16<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>165 \u2013 179<\/td>\r\n<td>28<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>180 \u2013 194<\/td>\r\n<td>12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>195 \u2013 209<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>210 \u2013 224<\/td>\r\n<td>7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>225 \u2013 239<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>240 \u2013 254<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>255 - 269<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nA histogram of this data would look like:\r\n\r\n<img class=\"aligncenter wp-image-416\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180850\/bluehistogram.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0-30. Horizontal measures Weights (pounds), in increments of 15 from 120-270. Measurements are noted between the 15-pound ranges, so that everyone weighing between 165-180, for instance, falls in the same category of measurement.\" width=\"350\" height=\"240\" \/>\r\n\r\nIn many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.\r\n\r\n<img class=\"aligncenter wp-image-417 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180928\/weightsfreq.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0-30. Horizontal measures Weights (pounds), in increments of 15 from 120-270. Measurements are noted between the 15-pound ranges, so that everyone weighing between 165-180, for instance, falls in the same category of measurement.\" width=\"381\" height=\"178\" \/>\r\n\r\nThe following video walks through this example in more detail.\r\n\r\nhttps:\/\/youtu.be\/JhshitTtdP0\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]6995[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nThe total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.\r\n\r\n$140\u00a0\u00a0\u00a0 $160\u00a0\u00a0\u00a0 $160\u00a0\u00a0\u00a0 $165\u00a0\u00a0\u00a0 $180\u00a0\u00a0\u00a0 $220\u00a0\u00a0\u00a0 $235\u00a0\u00a0\u00a0 $240\u00a0\u00a0\u00a0 $250\u00a0\u00a0\u00a0 $260\u00a0\u00a0\u00a0 $280\u00a0\u00a0\u00a0 $285\r\n\r\n$285\u00a0\u00a0\u00a0 $285\u00a0\u00a0\u00a0 $290\u00a0\u00a0\u00a0 $300\u00a0\u00a0\u00a0 $300\u00a0\u00a0\u00a0 $305\u00a0\u00a0\u00a0 $310\u00a0\u00a0\u00a0 $310\u00a0\u00a0\u00a0 $315\u00a0\u00a0\u00a0 $315\u00a0\u00a0\u00a0 $320\u00a0\u00a0\u00a0 $320\r\n\r\n$330\u00a0\u00a0\u00a0 $340\u00a0\u00a0\u00a0 $345\u00a0\u00a0\u00a0 $350\u00a0\u00a0\u00a0 $355\u00a0\u00a0\u00a0 $360\u00a0\u00a0\u00a0 $360\u00a0\u00a0\u00a0 $380\u00a0\u00a0\u00a0 $395\u00a0\u00a0\u00a0 $420\u00a0\u00a0\u00a0 $460\u00a0\u00a0\u00a0 $460\r\n\r\n<\/div>\r\nWhen collecting data to compare two groups, it is desirable to create a graph that compares quantities.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Interval (milliseconds)<\/strong><\/td>\r\n<td><strong>Frequency <\/strong><strong>small target<\/strong><\/td>\r\n<td><strong>Frequency\u00a0<\/strong><strong>large target<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>300-399<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>400-499<\/td>\r\n<td>1<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>500-599<\/td>\r\n<td>3<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>600-699<\/td>\r\n<td>6<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>700-799<\/td>\r\n<td>5<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>800-899<\/td>\r\n<td>4<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>900-999<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1000-1099<\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1100-1199<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOne option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.\r\n\r\n<img class=\"aligncenter wp-image-419 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12182203\/smalltargetlargetarget.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 2 from 0-10. Horizontal measures Reaction time (milliseconds), in increments of 100 from 300-399 to 1100-1199. Two colors of bars are given, noted by a key on the right: blue is small target, purple is large target. The large target is more dominant in 400-499 and 500-599 ranges, while the small target is noted in more columns and is more frequent in 600-699 and 700-799 milliseconds.\" width=\"430\" height=\"178\" \/>\r\n\r\n<\/div>\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Create a histogram that represents a data set<\/li>\n<\/ul>\n<\/div>\n<h2>Visualizing Numbers<\/h2>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/22162428\/numbers-738068_1280.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-952\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/22162428\/numbers-738068_1280-1024x576.jpg\" alt=\"Blue background with magnetic numbers attached to it. 1-5 are arranged sequentially at the top, while remaining digits are clustered at the bottom right\" width=\"1024\" height=\"576\" \/><\/a><\/p>\n<p>Quantitative, or numerical, data can also be summarized into frequency tables.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>The exam scores from 75 students were sorted from lowest to highest.<\/p>\n<p>32, 32, 33, 34, 38, 40, 41, 43, 44, 44, 45, 46, 47, 48, 48, 53, 53, 53, 54, 55, 55, 58, 59, 59, 59, 60, 60, 60, 64, 64, 64, 64, 65, 65, 65, 67, 67, 67, 67, 67, 68, 68, 68, 69, 69, 71, 72, 72, 72, 74, 74, 75, 75, 75, 77, 77, 78, 78, 79, 79, 80, 80, 80, 81, 83, 83, 84, 85, 86, 86, 90, 90, 91, 94, 97<\/p>\n<p>A <strong>frequency table<\/strong> can be created by grouping the scores in the following intervals: 30 \u2013 39, 40 \u2013 49, 50 \u2013 59, 60 \u2013 69, 70 \u2013 79, 80 \u2013 89, 90 \u2013 99.<\/p>\n<p style=\"text-align: center;\"><strong>Frequency Table of Exam Scores<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 84px;\">\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">Intervals of Scores<\/td>\n<td style=\"width: 50%; height: 12px;\">Frequency (or Count of Students Earning Scores in this Interval)<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">30 \u2013 39<\/td>\n<td style=\"width: 50%; height: 12px;\">5<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">40 \u2013 49<\/td>\n<td style=\"width: 50%; height: 12px;\">10<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">50 \u2013 59<\/td>\n<td style=\"width: 50%; height: 12px;\">10<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">60 \u2013 69<\/td>\n<td style=\"width: 50%; height: 12px;\">20<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">70 \u2013 79<\/td>\n<td style=\"width: 50%; height: 12px;\">15<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 50%; height: 12px;\">80 \u2013 89<\/td>\n<td style=\"width: 50%; height: 12px;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">90 \u2013 99<\/td>\n<td style=\"width: 50%;\">5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A graph can be created from the frequency table. This type of graph is called a <strong>histogram<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29224548\/Histogram.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6743 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29224548\/Histogram-300x187.jpg\" alt=\"\" width=\"693\" height=\"432\" \/><\/a><\/p>\n<\/div>\n<div><\/div>\n<div class=\"textbox exercises\">\n<h3>DIFFERENCE BETWEEN BAR GRAPHS AND HISTOGRAMS<\/h3>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29230843\/Bar-v-Histo.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6747 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/29230843\/Bar-v-Histo.jpg\" alt=\"\" width=\"791\" height=\"496\" \/><\/a><\/p>\n<p>Histograms are different from bar graphs. The horizontal axis in a bar graph has categories. The horizontal axis in a histogram is a continuous number line. In addition, the bars in a bar graph do not touch, but the bars (also called <strong>classes<\/strong>) in histogram do touch.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox\">\n<p><strong>HISTOGRAM<\/strong><\/p>\n<p>A histogram is a graph where the horizontal axis is a continuous number line. Data are grouped into equally spaced intervals. The intervals are called <strong>classes<\/strong>. Rectangles are drawn to represent the classes. The height of the rectangle can either be the frequency (or count of the number of data points in each class) or it can be the <strong>relative frequency<\/strong> (the frequency divided by the total count).<\/p>\n<\/div>\n<p>Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.<\/p>\n<p>If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into <strong>class intervals<\/strong>.<\/p>\n<div class=\"textbox\">\n<h3>Class Intervals<\/h3>\n<p>Class intervals are groupings of the data. In general, we define class intervals so that<\/p>\n<ul>\n<li>each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.<\/li>\n<li>we have somewhere between 5 and 20 classes, typically, depending upon the number of data we\u2019re working with.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Oftentimes we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Interval<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>120 &#8211; 134<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>135 \u2013 149<\/td>\n<td>14<\/td>\n<\/tr>\n<tr>\n<td>150 \u2013 164<\/td>\n<td>16<\/td>\n<\/tr>\n<tr>\n<td>165 \u2013 179<\/td>\n<td>28<\/td>\n<\/tr>\n<tr>\n<td>180 \u2013 194<\/td>\n<td>12<\/td>\n<\/tr>\n<tr>\n<td>195 \u2013 209<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>210 \u2013 224<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>225 \u2013 239<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>240 \u2013 254<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>255 &#8211; 269<\/td>\n<td>3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A histogram of this data would look like:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-416\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180850\/bluehistogram.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0-30. Horizontal measures Weights (pounds), in increments of 15 from 120-270. Measurements are noted between the 15-pound ranges, so that everyone weighing between 165-180, for instance, falls in the same category of measurement.\" width=\"350\" height=\"240\" \/><\/p>\n<p>In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-417 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180928\/weightsfreq.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 5 from 0-30. Horizontal measures Weights (pounds), in increments of 15 from 120-270. Measurements are noted between the 15-pound ranges, so that everyone weighing between 165-180, for instance, falls in the same category of measurement.\" width=\"381\" height=\"178\" \/><\/p>\n<p>The following video walks through this example in more detail.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Defining class intervals for a frequency table or histogram\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JhshitTtdP0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm6995\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=6995&theme=oea&iframe_resize_id=ohm6995&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.<\/p>\n<p>$140\u00a0\u00a0\u00a0 $160\u00a0\u00a0\u00a0 $160\u00a0\u00a0\u00a0 $165\u00a0\u00a0\u00a0 $180\u00a0\u00a0\u00a0 $220\u00a0\u00a0\u00a0 $235\u00a0\u00a0\u00a0 $240\u00a0\u00a0\u00a0 $250\u00a0\u00a0\u00a0 $260\u00a0\u00a0\u00a0 $280\u00a0\u00a0\u00a0 $285<\/p>\n<p>$285\u00a0\u00a0\u00a0 $285\u00a0\u00a0\u00a0 $290\u00a0\u00a0\u00a0 $300\u00a0\u00a0\u00a0 $300\u00a0\u00a0\u00a0 $305\u00a0\u00a0\u00a0 $310\u00a0\u00a0\u00a0 $310\u00a0\u00a0\u00a0 $315\u00a0\u00a0\u00a0 $315\u00a0\u00a0\u00a0 $320\u00a0\u00a0\u00a0 $320<\/p>\n<p>$330\u00a0\u00a0\u00a0 $340\u00a0\u00a0\u00a0 $345\u00a0\u00a0\u00a0 $350\u00a0\u00a0\u00a0 $355\u00a0\u00a0\u00a0 $360\u00a0\u00a0\u00a0 $360\u00a0\u00a0\u00a0 $380\u00a0\u00a0\u00a0 $395\u00a0\u00a0\u00a0 $420\u00a0\u00a0\u00a0 $460\u00a0\u00a0\u00a0 $460<\/p>\n<\/div>\n<p>When collecting data to compare two groups, it is desirable to create a graph that compares quantities.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Interval (milliseconds)<\/strong><\/td>\n<td><strong>Frequency <\/strong><strong>small target<\/strong><\/td>\n<td><strong>Frequency\u00a0<\/strong><strong>large target<\/strong><\/td>\n<\/tr>\n<tr>\n<td>300-399<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>400-499<\/td>\n<td>1<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>500-599<\/td>\n<td>3<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>600-699<\/td>\n<td>6<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>700-799<\/td>\n<td>5<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>800-899<\/td>\n<td>4<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>900-999<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1000-1099<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1100-1199<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-419 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12182203\/smalltargetlargetarget.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 2 from 0-10. Horizontal measures Reaction time (milliseconds), in increments of 100 from 300-399 to 1100-1199. Two colors of bars are given, noted by a key on the right: blue is small target, purple is large target. The large target is more dominant in 400-499 and 500-599 ranges, while the small target is noted in more columns and is more frequent in 600-699 and 700-799 milliseconds.\" width=\"430\" height=\"178\" \/><\/p>\n<\/div>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/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-413\">\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>Presenting Quantitative Data Graphically. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Math in Society. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>numbers-education-kindergarten. <strong>Authored by<\/strong>: karanja. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/numbers-education-kindergarten-738068\/\">https:\/\/pixabay.com\/en\/numbers-education-kindergarten-738068\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>Creating a histogram. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/180FgZ_cTrE\">https:\/\/youtu.be\/180FgZ_cTrE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Defining class intervals for a frequency table or histogram. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/JhshitTtdP0\">https:\/\/youtu.be\/JhshitTtdP0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>When not use a pie chart. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/FQ8zmZ56-XA\">https:\/\/youtu.be\/FQ8zmZ56-XA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Frequency polygons. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/rxByzA9MFFY\">https:\/\/youtu.be\/rxByzA9MFFY<\/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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":20,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Presenting Quantitative Data Graphically\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"Math in Society\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"numbers-education-kindergarten\",\"author\":\"karanja\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/numbers-education-kindergarten-738068\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Creating a histogram\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/180FgZ_cTrE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Defining class intervals for a frequency table or histogram\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/JhshitTtdP0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"When not use a pie chart\",\"author\":\"OCLPhase2\\'s 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