{"id":1140,"date":"2018-10-05T15:24:25","date_gmt":"2018-10-05T20:24:25","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=1140"},"modified":"2021-05-10T10:16:23","modified_gmt":"2021-05-10T15:16:23","slug":"mean","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/mean\/","title":{"rendered":"Visualizing the Mean (Average) of a Dataset"},"content":{"rendered":"<p><iframe loading=\"lazy\" title=\"Finding the Mean (Average) of a Dataset Visually | Measures of Central Tendency | Math Is Visual\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/0n7U2U2Ko2c?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>In this\u00a0<strong>Math Is Visual Prompt<\/strong>, students are given the opportunity to wrestle with the idea of the\u00a0<strong>mean\u00a0<\/strong>or\u00a0<strong>average\u00a0<\/strong>of a dataset visually.<\/p>\n<p>I was taught that you <a href=\"https:\/\/learn.makemathmoments.com\/task\/scavenger-hunt\" target=\"_blank\" rel=\"noopener noreferrer\">find the mean or average of a dataset<\/a> by adding up all of the values and dividing by the number of values. While that procedure will always work, I never understood the conceptual underpinnings of what I was actually doing.<\/p>\n<p>Let&#8217;s visualize the mean of a dataset by using square tiles to &#8220;redistribute&#8221; the extra tiles in the larger groups to the groups with less tiles. We then find the mean or average.<\/p>\n<p>Here we go!<\/p>\n<h2>Spark Curiosity: What Do You Notice? What Do You Wonder?<\/h2>\n<p>As I do in most every 3 act math task, I use the Annie Fetter &#8220;What do you notice? What do you wonder?&#8221; to spark curiosity while watching the first portion of <a href=\"https:\/\/youtu.be\/0n7U2U2Ko2c\">this video<\/a>.<\/p>\n<p>Here&#8217;s an image of what students\/children will be looking at when you are instructed to pause the video:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-1144\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-1024x576.jpeg\" alt=\"Measures of Central Tendency - Mean - What Do You Notice and Wonder Pause Video\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.012-What-Do-You-Notice-and-Wonder-Pause-Video.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>After students share what they notice and wonder, you can then show them the next portion of the video until you&#8217;re instructed to pause.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-1143\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-1024x576.jpeg\" alt=\"Measures of Central Tendency - Mean - How many squares would be in each group if they were shared fairly\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.016-How-many-squares-would-be-in-each-group-if-they-were-shared-fairly.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Here, students are asked to determine how many squares should each group have if they were shared fairly?<\/p>\n<p>While students will not know what this idea is called yet, what they are being asked to find is the <a href=\"https:\/\/learn.makemathmoments.com\/task\/scavenger-hunt\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>average\u00a0<\/strong>or the\u00a0<strong>mean\u00a0<\/strong>of the dataset<\/a>.<\/p>\n<p>They will redistribute the tiles to find that each group will end up with 9 squares.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-1142\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-1024x576.jpeg\" alt=\"Measures of Central Tendency - Mean - Solution - the mean of the data set\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/10\/Measures-of-Central-Tendency-Mean.020-Solution-the-mean-of-the-data-set.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Therefore, the\u00a0<strong>mean\u00a0<\/strong>or\u00a0<strong>average\u00a0<\/strong>of the dataset is 9 square tiles.<\/p>\n<p>&nbsp;<\/p>\n<h2>How&#8217;d It Go?<\/h2>\n<p>Thanks for watching and reading!<\/p>\n<p>Did you use this in your classroom or at home? How&#8217;d it go? Post in the comments!<\/p>\n<p><strong>Math IS Visual. Let&#8217;s teach it that way.<\/strong><\/p>\n<p>Dive into <a href=\"https:\/\/learn.makemathmoments.com\/tasks\" target=\"_blank\" rel=\"noopener\">conceptual 3 act math tasks<\/a>\u00a0that engage students and also develop procedural fluency throughout.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Were you told that you find the mean (average) of a dataset by adding the values and dividing by the number of values? Let&#8217;s explore visually!<\/p>\n","protected":false},"author":1,"featured_media":1143,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"footnotes":""},"categories":[56],"tags":[57,52,53],"series":[58],"class_list":["post-1140","post","type-post","status-publish","format-video","has-post-thumbnail","hentry","category-data-management-statistics","tag-grade-12","tag-grade-5","tag-grade-6","post_format-post-format-video","series-measures-of-central-tendency"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Visualizing the Mean (Average) of a Dataset | Central Tendency<\/title>\n<meta name=\"description\" content=\"Were you told that you find the mean (average) of a dataset by adding the values and dividing by the number of values? 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