{"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":"2021-02-06T00:02:09","modified_gmt":"2021-02-06T00:02:09","slug":"presenting-quantitative-data-graphically","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/presenting-quantitative-data-graphically\/","title":{"raw":"Presenting Quantitative Data Graphically","rendered":"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 \t<li>Analyze a frequency polygon graph that compares two variables<\/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 exercises\">\r\n<h3>Example<\/h3>\r\nA teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:\r\n\r\n19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0\r\n\r\nThese scores could be summarized into a frequency table by grouping like values:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Score<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>12<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>15<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>16<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>17<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>18<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>19<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>20<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nUsing the table from the first example, it would be possible to create a standard bar chart from this summary, like we did for categorical data:\r\n\r\n<img class=\"aligncenter wp-image-414\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180626\/frequencyscorebar.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 1 from 0-8. Horizontal measures Score, in irregular increments from 0-20. 18 is the highest frequency score, at 8, while 5 and 12 are the lowest frequency scores, at 1 each.\" width=\"350\" height=\"212\" \/>\r\nHowever, since the scores are numerical values, this chart doesn\u2019t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a <strong>histogram<\/strong>.\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Histogram<\/h3>\r\nA histogram is like a bar graph, but where the horizontal axis is a number line.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFor the values above, a histogram would look like:\r\n\r\n<img class=\"aligncenter wp-image-415\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180712\/frequencyscoreblue.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 1 from 0-9. Horizontal measures Score, in increments of 1 from 0-21. This includes several empty scores, denoting 0 frequency, while keeping data of earlier bar graph on this page.\" width=\"350\" height=\"240\" \/>\r\n\r\nNotice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at \u00bd values to avoid this ambiguity.\r\n\r\nThis video demonstrates the creation of the histogram from this data.\r\n\r\nhttps:\/\/youtu.be\/180FgZ_cTrE\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\nOther graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.\r\n\r\n<img class=\"aligncenter wp-image-418\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12181011\/weightspie.png\" alt=\"Pie graph, Weights (pounds). 10 colors are noted with a key on the right side. The biggest slice is aqua, for 165-179.\" width=\"350\" height=\"275\" \/>\r\n\r\nTo see more about why a pie chart isn't useful in this case, watch the following.\r\n\r\nhttps:\/\/youtu.be\/FQ8zmZ56-XA\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<\/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<div class=\"textbox\">\r\n<h3>Frequency polygon<\/h3>\r\nAn alternative representation is a <strong>frequency polygon<\/strong>. A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThis graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.\r\n\r\n<img class=\"aligncenter wp-image-420 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12182246\/smalltargetlargetarget2.png\" alt=\"Line graph. Vertical measures Frequency, in increments of 2 from 0-10. Horizontal measures Reaction time (milliseconds), in increments of 100 from 350-1150. Large target, depicted in pink, shows a dramatic increase and decrease, spiking at 550. Small target, in blue, shows a more erratic progression, gradually increasing to 650 and decreasing with bumps after.\" width=\"438\" height=\"178\" \/>\r\n\r\nThe following video explains frequency polygon creation for this example.\r\n\r\nhttps:\/\/youtu.be\/rxByzA9MFFY\r\n\r\n<\/div>","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<li>Analyze a frequency polygon graph that compares two variables<\/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 exercises\">\n<h3>Example<\/h3>\n<p>A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:<\/p>\n<p>19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0<\/p>\n<p>These scores could be summarized into a frequency table by grouping like values:<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Score<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>17<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>18<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>19<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td>6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Using the table from the first example, it would be possible to create a standard bar chart from this summary, like we did for categorical data:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-414\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180626\/frequencyscorebar.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 1 from 0-8. Horizontal measures Score, in irregular increments from 0-20. 18 is the highest frequency score, at 8, while 5 and 12 are the lowest frequency scores, at 1 each.\" width=\"350\" height=\"212\" \/><br \/>\nHowever, since the scores are numerical values, this chart doesn\u2019t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a <strong>histogram<\/strong>.<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Histogram<\/h3>\n<p>A histogram is like a bar graph, but where the horizontal axis is a number line.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>For the values above, a histogram would look like:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-415\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12180712\/frequencyscoreblue.png\" alt=\"Bar graph. Vertical measures Frequency, in increments of 1 from 0-9. Horizontal measures Score, in increments of 1 from 0-21. This includes several empty scores, denoting 0 frequency, while keeping data of earlier bar graph on this page.\" width=\"350\" height=\"240\" \/><\/p>\n<p>Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at \u00bd values to avoid this ambiguity.<\/p>\n<p>This video demonstrates the creation of the histogram from this data.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Creating a histogram\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/180FgZ_cTrE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-2\" 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>Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-418\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12181011\/weightspie.png\" alt=\"Pie graph, Weights (pounds). 10 colors are noted with a key on the right side. The biggest slice is aqua, for 165-179.\" width=\"350\" height=\"275\" \/><\/p>\n<p>To see more about why a pie chart isn&#8217;t useful in this case, watch the following.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"When not use a pie chart\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/FQ8zmZ56-XA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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<\/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<div class=\"textbox\">\n<h3>Frequency polygon<\/h3>\n<p>An alternative representation is a <strong>frequency polygon<\/strong>. A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-420 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12182246\/smalltargetlargetarget2.png\" alt=\"Line graph. Vertical measures Frequency, in increments of 2 from 0-10. Horizontal measures Reaction time (milliseconds), in increments of 100 from 350-1150. Large target, depicted in pink, shows a dramatic increase and decrease, spiking at 550. Small target, in blue, shows a more erratic progression, gradually increasing to 650 and decreasing with bumps after.\" width=\"438\" height=\"178\" \/><\/p>\n<p>The following video explains frequency polygon creation for this example.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Frequency polygons\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/rxByzA9MFFY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-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":9,"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 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