{"id":650,"date":"2021-08-13T14:33:01","date_gmt":"2021-08-13T14:33:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=650"},"modified":"2023-12-05T08:51:07","modified_gmt":"2023-12-05T08:51:07","slug":"stem-and-leaf-graphs-stemplots-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/stem-and-leaf-graphs-stemplots-2\/","title":{"raw":"Line Graphs","rendered":"Line Graphs"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul id=\"list123523\">\r\n \t<li>Construct a line graph<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall:\u00a0COORDINATE PLANE<\/h3>\r\nThe intersecting <i>x-<\/i> and <i>y-<\/i>axes of the coordinate plane divide it\u00a0into four sections. These four sections are called <b>quadrants<\/b>. Quadrants are named using the Roman numerals I, II, III, and IV, beginning with the top right quadrant and moving counter clockwise.\r\n<div class=\"textbox shaded\">\r\n<h3>The rectangular coordinate system<\/h3>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064227\/image002.jpg\" alt=\"A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.\" width=\"417\" height=\"378\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall:\u00a0Plotting Points<\/h3>\r\nA point (also called an ordered pair) has two values: \u201cThe first value is called the <em>x<\/em>-coordinate and the second value is the <em>y<\/em>-coordinate.\u201d\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224718\/CNX_BMath_Figure_11_01_027_img.png\" alt=\"The ordered pair x y is labeled with the first coordinate x labeled as \" \/>\r\n\r\nTo plot a point, you go along the x-axis and find the value of the <em>x<\/em>-coordinate and then go along the <em>y<\/em>-axis and find the value of the <em>y<\/em>-coordinate.\r\n\r\nLet\u2019s try locating the point [latex]\\left(2,5\\right)[\/latex]. In this ordered pair, the [latex]x[\/latex]-coordinate is [latex]2[\/latex] and the [latex]y[\/latex]-coordinate is [latex]5[\/latex].\r\n\r\nWe start by locating the [latex]x[\/latex] value, [latex]2[\/latex], on the [latex]x\\text{-axis.}[\/latex] Then we lightly sketch a vertical line through [latex]x=2[\/latex], as shown in the image 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\/24224719\/CNX_BMath_Figure_11_01_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There is a vertical dotted line passing through 2 on the x-axis.\" \/>\r\nNow we locate the [latex]y[\/latex] value, [latex]5[\/latex], on the [latex]y[\/latex] -axis and sketch a horizontal line through [latex]y=5[\/latex]. The point where these two lines meet is the point with coordinates [latex]\\left(2,5\\right)[\/latex]. We plot the point there, as shown in the image 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\/24224721\/CNX_BMath_Figure_11_01_005.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. An arrow starts at the end of the first arrow at 2 on the x-axis and goes vertically 5 units to a point labeled \" \/>\r\n\r\n<span style=\"color: #ff0000;\">Reminder:<\/span>\u00a0Any ordered pair, such as (2,5), represents one single point on the graph.\r\n\r\n<\/div>\r\nAnother type of graph that is useful for specific data values is a\u00a0<strong>line graph<\/strong>. In the particular line graph shown in the next example, the\u00a0<strong><em data-effect=\"italics\">x<\/em>-axis<\/strong>\u00a0(horizontal axis) consists of\u00a0data values\u00a0and the\u00a0<strong><em data-effect=\"italics\">y<\/em>-axis<\/strong>\u00a0(vertical axis) consists of\u00a0frequency points. The frequency points are connected using line segments.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIn a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in the table and figure below.\r\n<table summary=\"Table 2.7 \" data-id=\"M01_Ch02_tbl008\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">Number of times teenager is reminded<\/th>\r\n<th scope=\"col\">Frequency<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>14<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter wp-image-126 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/08181321\/0b1905558e3a48a1d8026a10062a7ea0b3cf81e01.jpeg\" alt=\"A line graph showing the number of times a teenager needs to be reminded to do chores on the x-axis and frequency on the y-axis.\" width=\"487\" height=\"306\" \/>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nIn a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The results are shown in the table below. Construct a line graph.\r\n<table summary=\"Table 2.8 \" data-id=\"M01_Ch02_tbl009\">\r\n<thead>\r\n<tr>\r\n<th scope=\"col\">Number of times in shop<\/th>\r\n<th scope=\"col\">Frequency<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td>7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>14<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul id=\"list123523\">\n<li>Construct a line graph<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall:\u00a0COORDINATE PLANE<\/h3>\n<p>The intersecting <i>x-<\/i> and <i>y-<\/i>axes of the coordinate plane divide it\u00a0into four sections. These four sections are called <b>quadrants<\/b>. Quadrants are named using the Roman numerals I, II, III, and IV, beginning with the top right quadrant and moving counter clockwise.<\/p>\n<div class=\"textbox shaded\">\n<h3>The rectangular coordinate system<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064227\/image002.jpg\" alt=\"A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.\" width=\"417\" height=\"378\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall:\u00a0Plotting Points<\/h3>\n<p>A point (also called an ordered pair) has two values: \u201cThe first value is called the <em>x<\/em>-coordinate and the second value is the <em>y<\/em>-coordinate.\u201d<\/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\/24224718\/CNX_BMath_Figure_11_01_027_img.png\" alt=\"The ordered pair x y is labeled with the first coordinate x labeled as\" \/><\/p>\n<p>To plot a point, you go along the x-axis and find the value of the <em>x<\/em>-coordinate and then go along the <em>y<\/em>-axis and find the value of the <em>y<\/em>-coordinate.<\/p>\n<p>Let\u2019s try locating the point [latex]\\left(2,5\\right)[\/latex]. In this ordered pair, the [latex]x[\/latex]-coordinate is [latex]2[\/latex] and the [latex]y[\/latex]-coordinate is [latex]5[\/latex].<\/p>\n<p>We start by locating the [latex]x[\/latex] value, [latex]2[\/latex], on the [latex]x\\text{-axis.}[\/latex] Then we lightly sketch a vertical line through [latex]x=2[\/latex], as shown in the image 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\/24224719\/CNX_BMath_Figure_11_01_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There is a vertical dotted line passing through 2 on the x-axis.\" \/><br \/>\nNow we locate the [latex]y[\/latex] value, [latex]5[\/latex], on the [latex]y[\/latex] -axis and sketch a horizontal line through [latex]y=5[\/latex]. The point where these two lines meet is the point with coordinates [latex]\\left(2,5\\right)[\/latex]. We plot the point there, as shown in the image 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\/24224721\/CNX_BMath_Figure_11_01_005.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. An arrow starts at the end of the first arrow at 2 on the x-axis and goes vertically 5 units to a point labeled\" \/><\/p>\n<p><span style=\"color: #ff0000;\">Reminder:<\/span>\u00a0Any ordered pair, such as (2,5), represents one single point on the graph.<\/p>\n<\/div>\n<p>Another type of graph that is useful for specific data values is a\u00a0<strong>line graph<\/strong>. In the particular line graph shown in the next example, the\u00a0<strong><em data-effect=\"italics\">x<\/em>-axis<\/strong>\u00a0(horizontal axis) consists of\u00a0data values\u00a0and the\u00a0<strong><em data-effect=\"italics\">y<\/em>-axis<\/strong>\u00a0(vertical axis) consists of\u00a0frequency points. The frequency points are connected using line segments.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in the table and figure below.<\/p>\n<table summary=\"Table 2.7\" data-id=\"M01_Ch02_tbl008\">\n<thead>\n<tr>\n<th scope=\"col\">Number of times teenager is reminded<\/th>\n<th scope=\"col\">Frequency<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>14<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-126 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/08181321\/0b1905558e3a48a1d8026a10062a7ea0b3cf81e01.jpeg\" alt=\"A line graph showing the number of times a teenager needs to be reminded to do chores on the x-axis and frequency on the y-axis.\" width=\"487\" height=\"306\" \/><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>In a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The results are shown in the table below. Construct a line graph.<\/p>\n<table summary=\"Table 2.8\" data-id=\"M01_Ch02_tbl009\">\n<thead>\n<tr>\n<th scope=\"col\">Number of times in shop<\/th>\n<th scope=\"col\">Frequency<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>14<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-650\">\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>OpenStax, Statistics, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs<\/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=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/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\/introductory-statistics\/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":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"OpenStax, Statistics, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs\",\"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\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at 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