{"id":72,"date":"2016-04-21T22:43:46","date_gmt":"2016-04-21T22:43:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=72"},"modified":"2021-07-04T16:33:11","modified_gmt":"2021-07-04T16:33:11","slug":"stem-and-leaf-graphs-stemplots","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/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 <strong>final significant digit<\/strong>. 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 to 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\nhttps:\/\/www.youtube.com\/watch?v=839OzHIsI-E\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/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<table style=\"width: 419px; height: 312px;\">\r\n<thead>\r\n<tr style=\"height: 12px;\">\r\n<th style=\"width: 406.641px; height: 12px; text-align: center;\" colspan=\"3\">Atlanta Hawks Wins and Losses<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 158.852px; text-align: center;\"><strong>Number of Wins<\/strong><\/td>\r\n<td style=\"width: 71.0781px;\"><\/td>\r\n<td style=\"width: 153.992px; text-align: center;\"><strong>Number of Losses<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"text-align: right; width: 158.852px; height: 12px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 12px; text-align: center;\">[latex]1[\/latex]<\/td>\r\n<td style=\"width: 153.992px; height: 12px;\">[latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 36px;\">\r\n<td style=\"text-align: right; width: 158.852px; height: 36px;\">[latex]9[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]6[\/latex] [latex]5[\/latex]<\/td>\r\n<td style=\"width: 71.0781px; height: 36px; text-align: center;\">[latex]2[\/latex]<\/td>\r\n<td style=\"width: 153.992px; height: 36px;\">[latex]5[\/latex] [latex]5[\/latex] [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 84px;\">\r\n<td style=\"text-align: right; width: 158.852px; height: 84px;\">[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: 84px; text-align: center;\">[latex]3[\/latex]<\/td>\r\n<td style=\"width: 153.992px; height: 84px;\">[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: 84px;\">\r\n<td style=\"text-align: right; width: 158.852px; height: 84px;\">[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: 84px; text-align: center;\">[latex]4[\/latex]<\/td>\r\n<td style=\"width: 153.992px; height: 84px;\">[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: 60px;\">\r\n<td style=\"text-align: right; width: 158.852px; height: 60px;\">[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: 60px; text-align: center;\">[latex]5[\/latex]<\/td>\r\n<td style=\"width: 153.992px; height: 60px;\">[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: 158.852px; height: 12px;\"><\/td>\r\n<td style=\"width: 71.0781px; height: 12px; text-align: center;\">[latex]6[\/latex]<\/td>\r\n<td style=\"width: 153.992px; 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 <strong>final significant digit<\/strong>. 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 to 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\" id=\"oembed-1\" title=\"\u2756 Stem and Leaf Plots \/ Stemplots \u2756\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/839OzHIsI-E?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/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<table style=\"width: 419px; height: 312px;\">\n<thead>\n<tr style=\"height: 12px;\">\n<th style=\"width: 406.641px; height: 12px; text-align: center;\" colspan=\"3\">Atlanta Hawks Wins and Losses<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 158.852px; text-align: center;\"><strong>Number of Wins<\/strong><\/td>\n<td style=\"width: 71.0781px;\"><\/td>\n<td style=\"width: 153.992px; text-align: center;\"><strong>Number of Losses<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"text-align: right; width: 158.852px; height: 12px;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 12px; text-align: center;\">[latex]1[\/latex]<\/td>\n<td style=\"width: 153.992px; height: 12px;\">[latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; width: 158.852px; height: 36px;\">[latex]9[\/latex] [latex]8[\/latex] [latex]8[\/latex] [latex]6[\/latex] [latex]5[\/latex]<\/td>\n<td style=\"width: 71.0781px; height: 36px; text-align: center;\">[latex]2[\/latex]<\/td>\n<td style=\"width: 153.992px; height: 36px;\">[latex]5[\/latex] [latex]5[\/latex] [latex]9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 84px;\">\n<td style=\"text-align: right; width: 158.852px; height: 84px;\">[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: 84px; text-align: center;\">[latex]3[\/latex]<\/td>\n<td style=\"width: 153.992px; height: 84px;\">[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: 84px;\">\n<td style=\"text-align: right; width: 158.852px; height: 84px;\">[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: 84px; text-align: center;\">[latex]4[\/latex]<\/td>\n<td style=\"width: 153.992px; height: 84px;\">[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: 60px;\">\n<td style=\"text-align: right; width: 158.852px; height: 60px;\">[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: 60px; text-align: center;\">[latex]5[\/latex]<\/td>\n<td style=\"width: 153.992px; height: 60px;\">[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: 158.852px; height: 12px;\"><\/td>\n<td style=\"width: 71.0781px; height: 12px; text-align: center;\">[latex]6[\/latex]<\/td>\n<td style=\"width: 153.992px; 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-72\">\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>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.34:10\/Introductory_Statistics\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.34:10\/Introductory_Statistics<\/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>Introductory Statistics . <strong>Authored by<\/strong>: Barbara Illowski, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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>: Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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":21,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"OpenStax, Statistics, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs\",\"author\":\"\",\"organization\":\"\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.34:10\/Introductory_Statistics\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"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 Illowski, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-72","chapter","type-chapter","status-publish","hentry"],"part":69,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapters\/72","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":16,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapters\/72\/revisions"}],"predecessor-version":[{"id":2258,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapters\/72\/revisions\/2258"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/parts\/69"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapters\/72\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/wp\/v2\/media?parent=72"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=72"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/wp\/v2\/contributor?post=72"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-introstats1\/wp-json\/wp\/v2\/license?post=72"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}