{"id":33,"date":"2021-06-22T15:30:09","date_gmt":"2021-06-22T15:30:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/stem-and-leaf-graphs-stemplots\/"},"modified":"2023-12-05T08:50:44","modified_gmt":"2023-12-05T08:50:44","slug":"stem-and-leaf-graphs-stemplots","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/stem-and-leaf-graphs-stemplots\/","title":{"raw":"Stem-and-Leaf Graphs (Stemplots)","rendered":"Stem-and-Leaf Graphs (Stemplots)"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul id=\"list123523\">\r\n \t<li>Display data graphically and interpret graphs: stemplots, histograms, and box plots<\/li>\r\n<\/ul>\r\n<\/div>\r\nOne simple graph, the\u00a0<strong>stem-and-leaf graph<\/strong> or <strong>stemplot<\/strong>, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, [latex]23[\/latex] has stem two and leaf three. The number [latex]432[\/latex] has stem [latex]43[\/latex] and leaf two. Likewise, the number [latex]5,432[\/latex] has stem [latex]543[\/latex] and leaf two. The decimal [latex]9.3[\/latex] has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFor Susan Dean's spring pre-calculus class, scores for the first exam were as follows (smallest to largest):\r\n[latex]33[\/latex]; [latex]42[\/latex]; [latex]49[\/latex]; [latex]49[\/latex]; [latex]53[\/latex]; [latex]55[\/latex]; [latex]55[\/latex]; [latex]61[\/latex]; [latex]63[\/latex]; [latex]67[\/latex]; [latex]68[\/latex]; [latex]68[\/latex]; [latex]69[\/latex]; [latex]69[\/latex]; [latex]72[\/latex]; [latex]73[\/latex]; [latex]74[\/latex]; [latex]78[\/latex]; [latex]80[\/latex]; [latex]83[\/latex]; [latex]88[\/latex]; [latex]88[\/latex]; [latex]88[\/latex]; [latex]90[\/latex]; [latex]92[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]96[\/latex]; [latex]100[\/latex]\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Stem<\/th>\r\n<th>Leaf<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]2[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]3[\/latex] [latex]5[\/latex] [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]1[\/latex] [latex]3[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<td>[latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]3[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe stemplot shows that most scores fell in the [latex]60[\/latex]s, [latex]70[\/latex]s, [latex]80[\/latex]s, and [latex]90[\/latex]s. Eight out of the [latex]31[\/latex] scores or approximately [latex]26[\/latex]% ([latex]\\frac{8}{31}[\/latex]) were in the [latex]90[\/latex]s or [latex]100[\/latex], a fairly high number of As.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFor the Park City basketball team, scores for the last 30 games were as follows (smallest to largest):\r\n\r\n[latex]32[\/latex]; [latex]32[\/latex]; [latex]33[\/latex]; [latex]34[\/latex]; [latex]38[\/latex]; [latex]40[\/latex]; [latex]42[\/latex]; [latex]42[\/latex]; [latex]43[\/latex]; [latex]44[\/latex]; [latex]46[\/latex]; [latex]47[\/latex]; [latex]47[\/latex]; [latex]48[\/latex]; [latex]48[\/latex]; [latex]48[\/latex]; [latex]49[\/latex]; [latex]50[\/latex]; [latex]50[\/latex]; [latex]51[\/latex]; [latex]52[\/latex]; [latex]52[\/latex]; [latex]52[\/latex]; [latex]53[\/latex]; [latex]54[\/latex]; [latex]56[\/latex]; [latex]57[\/latex]; [latex]57[\/latex]; [latex]60[\/latex]; [latex]61[\/latex]\r\n\r\nConstruct a stem plot for the data.\r\n[reveal-answer q=\"283391\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283391\"]\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Stem<\/th>\r\n<th>Leaf<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]0[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An <strong>outlier <\/strong>is an observation of data that does not fit the rest of the data. It is sometimes called an <strong>extreme value<\/strong>. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down [latex]50[\/latex] instead of [latex]500[\/latex]) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:\r\n\r\n[latex]1.1[\/latex]; [latex]1.5[\/latex]; [latex]2.3[\/latex]; [latex]2.5[\/latex]; [latex]2.7[\/latex]; [latex]3.2[\/latex]; [latex]3.3[\/latex]; [latex]3.3[\/latex]; [latex]3.5[\/latex]; [latex]3.8[\/latex]; [latex]4.0[\/latex]; [latex]4.2[\/latex]; [latex]4.5[\/latex]; [latex]4.5[\/latex]; [latex]4.7[\/latex]; [latex]4.8[\/latex]; [latex]5.5[\/latex]; [latex]5.6[\/latex]; [latex]6.5[\/latex]; [latex]6.7[\/latex]; [latex]12.3[\/latex];\r\nDoes the data seem to have any concentration of values?\r\n<div class=\"textbox shaded\">\r\n<h3>NOTE<\/h3>\r\nThe leaves are to the right of the decimal.\r\n\r\n<\/div>\r\n[reveal-answer q=\"283393\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283393\"]\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Stem<\/th>\r\n<th>Leaf<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]1[\/latex] [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]3[\/latex] [latex]5[\/latex] [latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]2[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]5[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]5[\/latex] [latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]5[\/latex] [latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe value [latex]12.3[\/latex] may be an outlier. Values appear to concentrate at three and four kilometers.\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nThe following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data and identify any outliers.\r\n\r\n[latex]0.5[\/latex]; [latex]0.7[\/latex]; [latex]1.1[\/latex]; [latex]1.2[\/latex]; [latex]1.2[\/latex]; [latex]1.3[\/latex]; [latex]1.3[\/latex]; [latex]1.5[\/latex]; [latex]1.5[\/latex]; [latex]1.7[\/latex]; [latex]1.7[\/latex]; [latex]1.8[\/latex]; [latex]1.9[\/latex]; [latex]2.0[\/latex]; [latex]2.2[\/latex]; [latex]2.5[\/latex]; [latex]2.6[\/latex]; [latex]2.8[\/latex]; [latex]2.8[\/latex]; [latex]2.8[\/latex]; [latex]3.5[\/latex]; [latex]3.8[\/latex]; [latex]4.4[\/latex]; [latex]4.8[\/latex]; [latex]4.9[\/latex]; [latex]5.2[\/latex]; [latex]5.5[\/latex]; [latex]5.7[\/latex]; [latex]5.8[\/latex]; [latex]8.0[\/latex]\r\n[reveal-answer q=\"283392\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283392\"]\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Stem<\/th>\r\n<th>Leaf<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]5[\/latex] [latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]1[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]5[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]4[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]2[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe value [latex]8.0[\/latex] may be an outlier. Values appear to concentrate at one and two miles.\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWatch this video to see an example of how to create a stem plot.\r\n\r\n<iframe src=\"\/\/plugin.3playmedia.com\/show?mf=7115015&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=839OzHIsI-E&amp;video_target=tpm-plugin-nl2p92nk-839OzHIsI-E\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA <strong>side-by-side stem-and-leaf plot<\/strong> allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems. The two following tables show the ages of U.S. presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.\r\n\r\nPresidents' Ages at Inauguration:\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Washington<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>Lincoln<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<td>Hoover<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>J. Adams<\/td>\r\n<td>[latex]61[\/latex]<\/td>\r\n<td>A. Johnson<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>F. Roosevelt<\/td>\r\n<td>[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Jefferson<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>Grant<\/td>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>Truman<\/td>\r\n<td>[latex]60[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Madison<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>Hayes<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>Eisenhower<\/td>\r\n<td>[latex]62[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Monroe<\/td>\r\n<td>[latex]58[\/latex]<\/td>\r\n<td>Garfield<\/td>\r\n<td>[latex]49[\/latex]<\/td>\r\n<td>Kennedy<\/td>\r\n<td>[latex]43[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>J. Q. Adams<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>Arthur<\/td>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>L. Johnson<\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Jackson<\/td>\r\n<td>[latex]61[\/latex]<\/td>\r\n<td>Cleveland<\/td>\r\n<td>[latex]47[\/latex]<\/td>\r\n<td>Nixon<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Van Buren<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>B. Harrison<\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<td>Ford<\/td>\r\n<td>[latex]61[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>W. H. Harrison<\/td>\r\n<td>[latex]68[\/latex]<\/td>\r\n<td>Cleveland<\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<td>Carter<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Tyler<\/td>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>McKinley<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>Reagan<\/td>\r\n<td>[latex]69[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Polk<\/td>\r\n<td>[latex]49[\/latex]<\/td>\r\n<td>T. Roosevelt<\/td>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>G.H.W. Bush<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Taylor<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>Taft<\/td>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>Clinton<\/td>\r\n<td>[latex]47[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fillmore<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>Wilson<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>G. W. Bush<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Pierce<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>Harding<\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<td>Obama<\/td>\r\n<td>[latex]47[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Buchanan<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<td>Coolidge<\/td>\r\n<td>[latex]51[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPresidents' Ages at Death:\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<th>President<\/th>\r\n<th>Age<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Washington<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>Lincoln<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>Hoover<\/td>\r\n<td>[latex]90[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>J. Adams<\/td>\r\n<td>[latex]90[\/latex]<\/td>\r\n<td>A. Johnson<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>F. Roosevelt<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Jefferson<\/td>\r\n<td>[latex]83[\/latex]<\/td>\r\n<td>Grant<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>Truman<\/td>\r\n<td>[latex]88[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Madison<\/td>\r\n<td>[latex]85[\/latex]<\/td>\r\n<td>Hayes<\/td>\r\n<td>[latex]70[\/latex]<\/td>\r\n<td>Eisenhower<\/td>\r\n<td>[latex]78[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Monroe<\/td>\r\n<td>[latex]73[\/latex]<\/td>\r\n<td>Garfield<\/td>\r\n<td>[latex]49[\/latex]<\/td>\r\n<td>Kennedy<\/td>\r\n<td>[latex]46[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>J. Q. Adams<\/td>\r\n<td>[latex]80[\/latex]<\/td>\r\n<td>Arthur<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>L. Johnson<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Jackson<\/td>\r\n<td>[latex]78[\/latex]<\/td>\r\n<td>Cleveland<\/td>\r\n<td>[latex]71[\/latex]<\/td>\r\n<td>Nixon<\/td>\r\n<td>[latex]81[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Van Buren<\/td>\r\n<td>[latex]79[\/latex]<\/td>\r\n<td>B. Harrison<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<td>Ford<\/td>\r\n<td>[latex]93[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>W. H. Harrison<\/td>\r\n<td>[latex]68[\/latex]<\/td>\r\n<td>Cleveland<\/td>\r\n<td>[latex]71[\/latex]<\/td>\r\n<td>Reagan<\/td>\r\n<td>[latex]93[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Tyler<\/td>\r\n<td>[latex]71[\/latex]<\/td>\r\n<td>McKinley<\/td>\r\n<td>[latex]58[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Polk<\/td>\r\n<td>[latex]53[\/latex]<\/td>\r\n<td>T. Roosevelt<\/td>\r\n<td>[latex]60[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Taylor<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<td>Taft<\/td>\r\n<td>[latex]72[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fillmore<\/td>\r\n<td>[latex]74[\/latex]<\/td>\r\n<td>Wilson<\/td>\r\n<td>[latex]67[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Pierce<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>Harding<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Buchanan<\/td>\r\n<td>[latex]77[\/latex]<\/td>\r\n<td>Coolidge<\/td>\r\n<td>[latex]60[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nThe table shows the number of wins and losses the Atlanta Hawks have had in [latex]42[\/latex] seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Losses<\/th>\r\n<th>Wins<\/th>\r\n<th>Year<\/th>\r\n<th>Losses<\/th>\r\n<th>Wins<\/th>\r\n<th>Year<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]34[\/latex]<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>1968\u20131969<\/td>\r\n<td>[latex]41[\/latex]<\/td>\r\n<td>[latex]41[\/latex]<\/td>\r\n<td>1989\u20131990<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]34[\/latex]<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>1969\u20131970<\/td>\r\n<td>[latex]39[\/latex]<\/td>\r\n<td>[latex]43[\/latex]<\/td>\r\n<td>1990\u20131991<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>1970\u20131971<\/td>\r\n<td>[latex]44[\/latex]<\/td>\r\n<td>[latex]38[\/latex]<\/td>\r\n<td>1991\u20131992<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>1971\u20131972<\/td>\r\n<td>[latex]39[\/latex]<\/td>\r\n<td>[latex]43[\/latex]<\/td>\r\n<td>1992\u20131993<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>1972\u20131973<\/td>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>1993\u20131994<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]47[\/latex]<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<td>1973\u20131974<\/td>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>1994\u20131995<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>[latex]31[\/latex]<\/td>\r\n<td>1974\u20131975<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>1995\u20131996<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]53[\/latex]<\/td>\r\n<td>[latex]29[\/latex]<\/td>\r\n<td>1975\u20131976<\/td>\r\n<td>[latex]26[\/latex]<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>1996\u20131997<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>[latex]31[\/latex]<\/td>\r\n<td>1976\u20131977<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>1997\u20131998<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]41[\/latex]<\/td>\r\n<td>[latex]41[\/latex]<\/td>\r\n<td>1977\u20131978<\/td>\r\n<td>[latex]19[\/latex]<\/td>\r\n<td>[latex]31[\/latex]<\/td>\r\n<td>1998\u20131999<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]46[\/latex]<\/td>\r\n<td>1978\u20131979<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>[latex]28[\/latex]<\/td>\r\n<td>1999\u20132000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>1979\u20131980<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>2000\u20132001<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]51[\/latex]<\/td>\r\n<td>[latex]31[\/latex]<\/td>\r\n<td>1980\u20131981<\/td>\r\n<td>[latex]49[\/latex]<\/td>\r\n<td>[latex]33[\/latex]<\/td>\r\n<td>2001\u20132002<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>1981\u20131982<\/td>\r\n<td>[latex]47[\/latex]<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<td>2002\u20132003<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]39[\/latex]<\/td>\r\n<td>[latex]43[\/latex]<\/td>\r\n<td>1982\u20131983<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>[latex]28[\/latex]<\/td>\r\n<td>2003\u20132004<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>1983\u20131984<\/td>\r\n<td>[latex]69[\/latex]<\/td>\r\n<td>[latex]13[\/latex]<\/td>\r\n<td>2004\u20132005<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>[latex]34[\/latex]<\/td>\r\n<td>1984\u20131985<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>[latex]26[\/latex]<\/td>\r\n<td>2005\u20132006<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>1985\u20131986<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<td>[latex]30[\/latex]<\/td>\r\n<td>2006\u20132007<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>[latex]57[\/latex]<\/td>\r\n<td>1986\u20131987<\/td>\r\n<td>[latex]45[\/latex]<\/td>\r\n<td>[latex]37[\/latex]<\/td>\r\n<td>2007\u20132008<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>1987\u20131988<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<td>[latex]47[\/latex]<\/td>\r\n<td>2008\u20132009<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]30[\/latex]<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<td>1988\u20131989<\/td>\r\n<td>[latex]29[\/latex]<\/td>\r\n<td>[latex]53[\/latex]<\/td>\r\n<td>2009\u20132010<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"283394\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283394\"]\r\n\r\nNumber of Losses\r\n<table style=\"width: 532px; height: 323px;\">\r\n<thead>\r\n<tr style=\"height: 10px;\">\r\n<th style=\"width: 519.656px; text-align: center; height: 10px;\" colspan=\"3\">Atlanta Hawks Wins and Losses<\/th>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<th style=\"width: 236.984px; height: 12px;\">Number of Wins<\/th>\r\n<td style=\"width: 71.0781px; height: 12px;\"><\/td>\r\n<td style=\"width: 188.906px; height: 12px;\"><strong>Number of Losses<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: right; width: 236.984px; height: 12px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 12px;\">[latex]1[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 12px;\">[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 38px;\">\r\n<td style=\"text-align: right; width: 236.984px; height: 38px;\">[latex]9[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]6[\/latex] [latex]5[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 38px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 38px;\">[latex]5[\/latex] [latex]5[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 88px;\">\r\n<td style=\"text-align: right; width: 236.984px; height: 88px;\">[latex]8[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]4[\/latex] [latex]3[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]0[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 88px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 88px;\">[latex]0[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]9[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 88px;\">\r\n<td style=\"text-align: right; width: 236.984px; height: 88px;\">[latex]8[\/latex] [latex]8[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]0[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 88px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 88px;\">[latex]0[\/latex] [latex]0[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 63px;\">\r\n<td style=\"text-align: right; width: 236.984px; height: 63px;\">[latex]7[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]3[\/latex] [latex]2[\/latex] [latex]0[\/latex] [latex]0[\/latex] [latex]0[\/latex] [latex]0[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 63px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 63px;\">[latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 236.984px; height: 12px;\"><\/td>\r\n<td style=\"width: 71.0781px; height: 12px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 188.906px; height: 12px;\">[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul id=\"list123523\">\n<li>Display data graphically and interpret graphs: stemplots, histograms, and box plots<\/li>\n<\/ul>\n<\/div>\n<p>One simple graph, the\u00a0<strong>stem-and-leaf graph<\/strong> or <strong>stemplot<\/strong>, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, [latex]23[\/latex] has stem two and leaf three. The number [latex]432[\/latex] has stem [latex]43[\/latex] and leaf two. Likewise, the number [latex]5,432[\/latex] has stem [latex]543[\/latex] and leaf two. The decimal [latex]9.3[\/latex] has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>For Susan Dean&#8217;s spring pre-calculus class, scores for the first exam were as follows (smallest to largest):<br \/>\n[latex]33[\/latex]; [latex]42[\/latex]; [latex]49[\/latex]; [latex]49[\/latex]; [latex]53[\/latex]; [latex]55[\/latex]; [latex]55[\/latex]; [latex]61[\/latex]; [latex]63[\/latex]; [latex]67[\/latex]; [latex]68[\/latex]; [latex]68[\/latex]; [latex]69[\/latex]; [latex]69[\/latex]; [latex]72[\/latex]; [latex]73[\/latex]; [latex]74[\/latex]; [latex]78[\/latex]; [latex]80[\/latex]; [latex]83[\/latex]; [latex]88[\/latex]; [latex]88[\/latex]; [latex]88[\/latex]; [latex]90[\/latex]; [latex]92[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]94[\/latex]; [latex]96[\/latex]; [latex]100[\/latex]<\/p>\n<table>\n<thead>\n<tr>\n<th>Stem<\/th>\n<th>Leaf<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]2[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]3[\/latex] [latex]5[\/latex] [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]1[\/latex] [latex]3[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<td>[latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]3[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The stemplot shows that most scores fell in the [latex]60[\/latex]s, [latex]70[\/latex]s, [latex]80[\/latex]s, and [latex]90[\/latex]s. Eight out of the [latex]31[\/latex] scores or approximately [latex]26[\/latex]% ([latex]\\frac{8}{31}[\/latex]) were in the [latex]90[\/latex]s or [latex]100[\/latex], a fairly high number of As.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>For the Park City basketball team, scores for the last 30 games were as follows (smallest to largest):<\/p>\n<p>[latex]32[\/latex]; [latex]32[\/latex]; [latex]33[\/latex]; [latex]34[\/latex]; [latex]38[\/latex]; [latex]40[\/latex]; [latex]42[\/latex]; [latex]42[\/latex]; [latex]43[\/latex]; [latex]44[\/latex]; [latex]46[\/latex]; [latex]47[\/latex]; [latex]47[\/latex]; [latex]48[\/latex]; [latex]48[\/latex]; [latex]48[\/latex]; [latex]49[\/latex]; [latex]50[\/latex]; [latex]50[\/latex]; [latex]51[\/latex]; [latex]52[\/latex]; [latex]52[\/latex]; [latex]52[\/latex]; [latex]53[\/latex]; [latex]54[\/latex]; [latex]56[\/latex]; [latex]57[\/latex]; [latex]57[\/latex]; [latex]60[\/latex]; [latex]61[\/latex]<\/p>\n<p>Construct a stem plot for the data.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q283391\">Show Solution<\/span><\/p>\n<div id=\"q283391\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<thead>\n<tr>\n<th>Stem<\/th>\n<th>Leaf<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]0[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An <strong>outlier <\/strong>is an observation of data that does not fit the rest of the data. It is sometimes called an <strong>extreme value<\/strong>. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down [latex]50[\/latex] instead of [latex]500[\/latex]) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:<\/p>\n<p>[latex]1.1[\/latex]; [latex]1.5[\/latex]; [latex]2.3[\/latex]; [latex]2.5[\/latex]; [latex]2.7[\/latex]; [latex]3.2[\/latex]; [latex]3.3[\/latex]; [latex]3.3[\/latex]; [latex]3.5[\/latex]; [latex]3.8[\/latex]; [latex]4.0[\/latex]; [latex]4.2[\/latex]; [latex]4.5[\/latex]; [latex]4.5[\/latex]; [latex]4.7[\/latex]; [latex]4.8[\/latex]; [latex]5.5[\/latex]; [latex]5.6[\/latex]; [latex]6.5[\/latex]; [latex]6.7[\/latex]; [latex]12.3[\/latex];<br \/>\nDoes the data seem to have any concentration of values?<\/p>\n<div class=\"textbox shaded\">\n<h3>NOTE<\/h3>\n<p>The leaves are to the right of the decimal.<\/p>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q283393\">Show Solution<\/span><\/p>\n<div id=\"q283393\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<thead>\n<tr>\n<th>Stem<\/th>\n<th>Leaf<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]1[\/latex] [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]3[\/latex] [latex]5[\/latex] [latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]2[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]5[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]5[\/latex] [latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]5[\/latex] [latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The value [latex]12.3[\/latex] may be an outlier. Values appear to concentrate at three and four kilometers.\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data and identify any outliers.<\/p>\n<p>[latex]0.5[\/latex]; [latex]0.7[\/latex]; [latex]1.1[\/latex]; [latex]1.2[\/latex]; [latex]1.2[\/latex]; [latex]1.3[\/latex]; [latex]1.3[\/latex]; [latex]1.5[\/latex]; [latex]1.5[\/latex]; [latex]1.7[\/latex]; [latex]1.7[\/latex]; [latex]1.8[\/latex]; [latex]1.9[\/latex]; [latex]2.0[\/latex]; [latex]2.2[\/latex]; [latex]2.5[\/latex]; [latex]2.6[\/latex]; [latex]2.8[\/latex]; [latex]2.8[\/latex]; [latex]2.8[\/latex]; [latex]3.5[\/latex]; [latex]3.8[\/latex]; [latex]4.4[\/latex]; [latex]4.8[\/latex]; [latex]4.9[\/latex]; [latex]5.2[\/latex]; [latex]5.5[\/latex]; [latex]5.7[\/latex]; [latex]5.8[\/latex]; [latex]8.0[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q283392\">Show Solution<\/span><\/p>\n<div id=\"q283392\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<thead>\n<tr>\n<th>Stem<\/th>\n<th>Leaf<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]5[\/latex] [latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]1[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]0[\/latex] [latex]2[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]5[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]4[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]2[\/latex] [latex]5[\/latex] [latex]7[\/latex] [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The value [latex]8.0[\/latex] may be an outlier. Values appear to concentrate at one and two miles.\n<\/p><\/div>\n<\/div>\n<\/div>\n<p>Watch this video to see an example of how to create a stem plot.<\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=7115015&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=839OzHIsI-E&amp;video_target=tpm-plugin-nl2p92nk-839OzHIsI-E\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A <strong>side-by-side stem-and-leaf plot<\/strong> allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems. The two following tables show the ages of U.S. presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.<\/p>\n<p>Presidents&#8217; Ages at Inauguration:<\/p>\n<table>\n<thead>\n<tr>\n<th>President<\/th>\n<th>Age<\/th>\n<th>President<\/th>\n<th>Age<\/th>\n<th>President<\/th>\n<th>Age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Washington<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>Lincoln<\/td>\n<td>[latex]52[\/latex]<\/td>\n<td>Hoover<\/td>\n<td>[latex]54[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>J. Adams<\/td>\n<td>[latex]61[\/latex]<\/td>\n<td>A. Johnson<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>F. Roosevelt<\/td>\n<td>[latex]51[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Jefferson<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>Grant<\/td>\n<td>[latex]46[\/latex]<\/td>\n<td>Truman<\/td>\n<td>[latex]60[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Madison<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>Hayes<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>Eisenhower<\/td>\n<td>[latex]62[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Monroe<\/td>\n<td>[latex]58[\/latex]<\/td>\n<td>Garfield<\/td>\n<td>[latex]49[\/latex]<\/td>\n<td>Kennedy<\/td>\n<td>[latex]43[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>J. Q. Adams<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>Arthur<\/td>\n<td>[latex]51[\/latex]<\/td>\n<td>L. Johnson<\/td>\n<td>[latex]55[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Jackson<\/td>\n<td>[latex]61[\/latex]<\/td>\n<td>Cleveland<\/td>\n<td>[latex]47[\/latex]<\/td>\n<td>Nixon<\/td>\n<td>[latex]56[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Van Buren<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>B. Harrison<\/td>\n<td>[latex]55[\/latex]<\/td>\n<td>Ford<\/td>\n<td>[latex]61[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>W. H. Harrison<\/td>\n<td>[latex]68[\/latex]<\/td>\n<td>Cleveland<\/td>\n<td>[latex]55[\/latex]<\/td>\n<td>Carter<\/td>\n<td>[latex]52[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Tyler<\/td>\n<td>[latex]51[\/latex]<\/td>\n<td>McKinley<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>Reagan<\/td>\n<td>[latex]69[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Polk<\/td>\n<td>[latex]49[\/latex]<\/td>\n<td>T. Roosevelt<\/td>\n<td>[latex]42[\/latex]<\/td>\n<td>G.H.W. Bush<\/td>\n<td>[latex]64[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Taylor<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>Taft<\/td>\n<td>[latex]51[\/latex]<\/td>\n<td>Clinton<\/td>\n<td>[latex]47[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Fillmore<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>Wilson<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>G. W. Bush<\/td>\n<td>[latex]54[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Pierce<\/td>\n<td>[latex]48[\/latex]<\/td>\n<td>Harding<\/td>\n<td>[latex]55[\/latex]<\/td>\n<td>Obama<\/td>\n<td>[latex]47[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Buchanan<\/td>\n<td>[latex]65[\/latex]<\/td>\n<td>Coolidge<\/td>\n<td>[latex]51[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Presidents&#8217; Ages at Death:<\/p>\n<table>\n<thead>\n<tr>\n<th>President<\/th>\n<th>Age<\/th>\n<th>President<\/th>\n<th>Age<\/th>\n<th>President<\/th>\n<th>Age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Washington<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>Lincoln<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>Hoover<\/td>\n<td>[latex]90[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>J. Adams<\/td>\n<td>[latex]90[\/latex]<\/td>\n<td>A. Johnson<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>F. Roosevelt<\/td>\n<td>[latex]63[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Jefferson<\/td>\n<td>[latex]83[\/latex]<\/td>\n<td>Grant<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>Truman<\/td>\n<td>[latex]88[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Madison<\/td>\n<td>[latex]85[\/latex]<\/td>\n<td>Hayes<\/td>\n<td>[latex]70[\/latex]<\/td>\n<td>Eisenhower<\/td>\n<td>[latex]78[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Monroe<\/td>\n<td>[latex]73[\/latex]<\/td>\n<td>Garfield<\/td>\n<td>[latex]49[\/latex]<\/td>\n<td>Kennedy<\/td>\n<td>[latex]46[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>J. Q. Adams<\/td>\n<td>[latex]80[\/latex]<\/td>\n<td>Arthur<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>L. Johnson<\/td>\n<td>[latex]64[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Jackson<\/td>\n<td>[latex]78[\/latex]<\/td>\n<td>Cleveland<\/td>\n<td>[latex]71[\/latex]<\/td>\n<td>Nixon<\/td>\n<td>[latex]81[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Van Buren<\/td>\n<td>[latex]79[\/latex]<\/td>\n<td>B. Harrison<\/td>\n<td>[latex]67[\/latex]<\/td>\n<td>Ford<\/td>\n<td>[latex]93[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>W. H. Harrison<\/td>\n<td>[latex]68[\/latex]<\/td>\n<td>Cleveland<\/td>\n<td>[latex]71[\/latex]<\/td>\n<td>Reagan<\/td>\n<td>[latex]93[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Tyler<\/td>\n<td>[latex]71[\/latex]<\/td>\n<td>McKinley<\/td>\n<td>[latex]58[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Polk<\/td>\n<td>[latex]53[\/latex]<\/td>\n<td>T. Roosevelt<\/td>\n<td>[latex]60[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Taylor<\/td>\n<td>[latex]65[\/latex]<\/td>\n<td>Taft<\/td>\n<td>[latex]72[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Fillmore<\/td>\n<td>[latex]74[\/latex]<\/td>\n<td>Wilson<\/td>\n<td>[latex]67[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Pierce<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>Harding<\/td>\n<td>[latex]57[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Buchanan<\/td>\n<td>[latex]77[\/latex]<\/td>\n<td>Coolidge<\/td>\n<td>[latex]60[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>The table shows the number of wins and losses the Atlanta Hawks have had in [latex]42[\/latex] seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.<\/p>\n<table>\n<thead>\n<tr>\n<th>Losses<\/th>\n<th>Wins<\/th>\n<th>Year<\/th>\n<th>Losses<\/th>\n<th>Wins<\/th>\n<th>Year<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]34[\/latex]<\/td>\n<td>[latex]48[\/latex]<\/td>\n<td>1968\u20131969<\/td>\n<td>[latex]41[\/latex]<\/td>\n<td>[latex]41[\/latex]<\/td>\n<td>1989\u20131990<\/td>\n<\/tr>\n<tr>\n<td>[latex]34[\/latex]<\/td>\n<td>[latex]48[\/latex]<\/td>\n<td>1969\u20131970<\/td>\n<td>[latex]39[\/latex]<\/td>\n<td>[latex]43[\/latex]<\/td>\n<td>1990\u20131991<\/td>\n<\/tr>\n<tr>\n<td>[latex]46[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>1970\u20131971<\/td>\n<td>[latex]44[\/latex]<\/td>\n<td>[latex]38[\/latex]<\/td>\n<td>1991\u20131992<\/td>\n<\/tr>\n<tr>\n<td>[latex]46[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>1971\u20131972<\/td>\n<td>[latex]39[\/latex]<\/td>\n<td>[latex]43[\/latex]<\/td>\n<td>1992\u20131993<\/td>\n<\/tr>\n<tr>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]46[\/latex]<\/td>\n<td>1972\u20131973<\/td>\n<td>[latex]25[\/latex]<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>1993\u20131994<\/td>\n<\/tr>\n<tr>\n<td>[latex]47[\/latex]<\/td>\n<td>[latex]35[\/latex]<\/td>\n<td>1973\u20131974<\/td>\n<td>[latex]40[\/latex]<\/td>\n<td>[latex]42[\/latex]<\/td>\n<td>1994\u20131995<\/td>\n<\/tr>\n<tr>\n<td>[latex]51[\/latex]<\/td>\n<td>[latex]31[\/latex]<\/td>\n<td>1974\u20131975<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]46[\/latex]<\/td>\n<td>1995\u20131996<\/td>\n<\/tr>\n<tr>\n<td>[latex]53[\/latex]<\/td>\n<td>[latex]29[\/latex]<\/td>\n<td>1975\u20131976<\/td>\n<td>[latex]26[\/latex]<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>1996\u20131997<\/td>\n<\/tr>\n<tr>\n<td>[latex]51[\/latex]<\/td>\n<td>[latex]31[\/latex]<\/td>\n<td>1976\u20131977<\/td>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>1997\u20131998<\/td>\n<\/tr>\n<tr>\n<td>[latex]41[\/latex]<\/td>\n<td>[latex]41[\/latex]<\/td>\n<td>1977\u20131978<\/td>\n<td>[latex]19[\/latex]<\/td>\n<td>[latex]31[\/latex]<\/td>\n<td>1998\u20131999<\/td>\n<\/tr>\n<tr>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]46[\/latex]<\/td>\n<td>1978\u20131979<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>[latex]28[\/latex]<\/td>\n<td>1999\u20132000<\/td>\n<\/tr>\n<tr>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>1979\u20131980<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>[latex]25[\/latex]<\/td>\n<td>2000\u20132001<\/td>\n<\/tr>\n<tr>\n<td>[latex]51[\/latex]<\/td>\n<td>[latex]31[\/latex]<\/td>\n<td>1980\u20131981<\/td>\n<td>[latex]49[\/latex]<\/td>\n<td>[latex]33[\/latex]<\/td>\n<td>2001\u20132002<\/td>\n<\/tr>\n<tr>\n<td>[latex]40[\/latex]<\/td>\n<td>[latex]42[\/latex]<\/td>\n<td>1981\u20131982<\/td>\n<td>[latex]47[\/latex]<\/td>\n<td>[latex]35[\/latex]<\/td>\n<td>2002\u20132003<\/td>\n<\/tr>\n<tr>\n<td>[latex]39[\/latex]<\/td>\n<td>[latex]43[\/latex]<\/td>\n<td>1982\u20131983<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>[latex]28[\/latex]<\/td>\n<td>2003\u20132004<\/td>\n<\/tr>\n<tr>\n<td>[latex]42[\/latex]<\/td>\n<td>[latex]40[\/latex]<\/td>\n<td>1983\u20131984<\/td>\n<td>[latex]69[\/latex]<\/td>\n<td>[latex]13[\/latex]<\/td>\n<td>2004\u20132005<\/td>\n<\/tr>\n<tr>\n<td>[latex]48[\/latex]<\/td>\n<td>[latex]34[\/latex]<\/td>\n<td>1984\u20131985<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>[latex]26[\/latex]<\/td>\n<td>2005\u20132006<\/td>\n<\/tr>\n<tr>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>1985\u20131986<\/td>\n<td>[latex]52[\/latex]<\/td>\n<td>[latex]30[\/latex]<\/td>\n<td>2006\u20132007<\/td>\n<\/tr>\n<tr>\n<td>[latex]25[\/latex]<\/td>\n<td>[latex]57[\/latex]<\/td>\n<td>1986\u20131987<\/td>\n<td>[latex]45[\/latex]<\/td>\n<td>[latex]37[\/latex]<\/td>\n<td>2007\u20132008<\/td>\n<\/tr>\n<tr>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>1987\u20131988<\/td>\n<td>[latex]35[\/latex]<\/td>\n<td>[latex]47[\/latex]<\/td>\n<td>2008\u20132009<\/td>\n<\/tr>\n<tr>\n<td>[latex]30[\/latex]<\/td>\n<td>[latex]52[\/latex]<\/td>\n<td>1988\u20131989<\/td>\n<td>[latex]29[\/latex]<\/td>\n<td>[latex]53[\/latex]<\/td>\n<td>2009\u20132010<\/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=\"q283394\">Show Solution<\/span><\/p>\n<div id=\"q283394\" class=\"hidden-answer\" style=\"display: none\">\n<p>Number of Losses<\/p>\n<table style=\"width: 532px; height: 323px;\">\n<thead>\n<tr style=\"height: 10px;\">\n<th style=\"width: 519.656px; text-align: center; height: 10px;\" colspan=\"3\">Atlanta Hawks Wins and Losses<\/th>\n<\/tr>\n<tr style=\"height: 12px;\">\n<th style=\"width: 236.984px; height: 12px;\">Number of Wins<\/th>\n<td style=\"width: 71.0781px; height: 12px;\"><\/td>\n<td style=\"width: 188.906px; height: 12px;\"><strong>Number of Losses<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: right; width: 236.984px; height: 12px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 12px;\">[latex]1[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 12px;\">[latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 38px;\">\n<td style=\"text-align: right; width: 236.984px; height: 38px;\">[latex]9[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]6[\/latex] [latex]5[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 38px;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 38px;\">[latex]5[\/latex] [latex]5[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 88px;\">\n<td style=\"text-align: right; width: 236.984px; height: 88px;\">[latex]8[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]5[\/latex] [latex]5[\/latex] [latex]4[\/latex] [latex]3[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]0[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 88px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 88px;\">[latex]0[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]9[\/latex] [latex]9[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 88px;\">\n<td style=\"text-align: right; width: 236.984px; height: 88px;\">[latex]8[\/latex] [latex]8[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]3[\/latex] [latex]2[\/latex] [latex]2[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]0[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 88px;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 88px;\">[latex]0[\/latex] [latex]0[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]4[\/latex] [latex]5[\/latex] [latex]6[\/latex] [latex]6[\/latex] [latex]7[\/latex] [latex]7[\/latex] [latex]8[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 63px;\">\n<td style=\"text-align: right; width: 236.984px; height: 63px;\">[latex]7[\/latex] [latex]7[\/latex] [latex]6[\/latex] [latex]3[\/latex] [latex]2[\/latex] [latex]0[\/latex] [latex]0[\/latex] [latex]0[\/latex] [latex]0[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 63px;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 63px;\">[latex]1[\/latex] [latex]1[\/latex] [latex]1[\/latex] [latex]2[\/latex] [latex]3[\/latex] [latex]4[\/latex] [latex]4[\/latex] [latex]6[\/latex] [latex]7[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 236.984px; height: 12px;\"><\/td>\n<td style=\"width: 71.0781px; height: 12px;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 188.906px; height: 12px;\">[latex]9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\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-33\">\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 class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Stem and Leaf Plots aka Stemplots. <strong>Authored by<\/strong>: patrickJMT. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.youtube.com\/watch?v=839OzHIsI-E\">https:\/\/www.youtube.com\/watch?v=839OzHIsI-E<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/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":17533,"menu_order":9,"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\":\"copyrighted_video\",\"description\":\"Stem and Leaf Plots aka Stemplots\",\"author\":\"patrickJMT\",\"organization\":\"\",\"url\":\"https:\/\/www.youtube.com\/watch?v=839OzHIsI-E\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"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 https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-33","chapter","type-chapter","status-publish","hentry"],"part":31,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":23,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/33\/revisions"}],"predecessor-version":[{"id":3481,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/33\/revisions\/3481"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/31"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/33\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=33"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=33"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=33"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}