{"id":61997,"date":"2020-10-12T15:32:46","date_gmt":"2020-10-12T15:32:46","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=61997"},"modified":"2026-03-28T10:32:04","modified_gmt":"2026-03-28T15:32:04","slug":"statistical-range","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/statistical-range\/","title":{"rendered":"Statistical Range"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_8sFXb5szvHg\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_8sFXb5szvHg\" data-source-videoID=\"8sFXb5szvHg\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Statistical Range Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Statistical Range\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_8sFXb5szvHg:hover {cursor:pointer;} img#videoThumbnailImage_8sFXb5szvHg {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1745-statistical-range-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_8sFXb5szvHg\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_8sFXb5szvHg\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Statistical Range\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_8sFXb5szvHg\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_8sFXb5szvHg\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_8sFXb5szvHg\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction z2v_Function() {\n  var x = document.getElementById(\"z2v\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"z2v_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"z2v\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_Range\" class=\"smooth-scroll\">What is Range?<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Mean,_Median,_and_Mode\" class=\"smooth-scroll\">Mean, Median, and Mode<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Find_Range\" class=\"smooth-scroll\">How to Find Range<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Statistical_Range_Practice_Questions\" class=\"smooth-scroll\">Statistical Range Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on range!<\/p>\n<h2><span id=\"What_is_Range\" class=\"m-toc-anchor\"><\/span>What is Range?<\/h2>\n<p>\nRange has two different definitions in math: the outputs of a function, or the difference between the highest and lowest values in a set of numbers. In this video, we will be talking about the second definition.<\/p>\n<h3><span id=\"Mean,_Median,_and_Mode\" class=\"m-toc-anchor\"><\/span>Mean, Median, and Mode<\/h3>\n<p>\nRange is one of four important values used in basic statistics. The other three are <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/mean-median-and-mode\/\">mean, median, and mode<\/a>. Range tells you how big the spread of values is, meaning how far apart your largest and smallest values are. <\/p>\n<p>This is helpful in knowing how accurate your results are. For example, if your teacher gives the class a test and the highest grade is a 100, while the lowest grade is a 12, the range would be 88, which is pretty large for a test with a max score of 100.<\/p>\n<p>The range is useful for knowing the accuracy of results, but usually can\u2019t be used alone. It\u2019s most useful when combined with one of the other three values. In our test example, knowing that there is such a large range could mean that the students scored all over the place: some really high and some really low, which would tell the teacher that he or she didn\u2019t explain the information in a way that everyone could understand. But the teacher could get the same range of scores if everyone in the class got an A on the test but one person failed with a 12. The one person with a 12 is called an outlier, because he or she is not part of the normal grades for the class.<\/p>\n<p>This is why knowing one of the other important values, especially the mean, is useful in interpreting the data. A low mean, or one in the middle, would give us the first conclusion, that the teacher could have explained things better in order for the whole class to understand. A high mean would give us the second conclusion, that most of the class did really well and understood the concept with a couple of outliers who may need some one-on-one help, but the teacher is able to move on to the next lesson.<\/p>\n<h2><span id=\"How_to_Find_Range\" class=\"m-toc-anchor\"><\/span>How to Find Range<\/h2>\n<p>\nThe range for a set of data is found by subtracting the smallest value from the largest value.<\/p>\n<p>Let\u2019s take a look at a few examples.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWhat is the range of this set of data?<\/p>\n<div class=\"examplesentence\">{2, 13, 21, 19, 43, 4, 7, and 16}<\/div>\n<p>\n&nbsp;<br \/>\nRemember, for range all we need to know is the highest and lowest values. The highest value in this set is 43 and the lowest value is 2.<\/p>\n<div class=\"examplesentence\">\\(43 \u2013 2 = 41\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur range is 41, which is fairly large for this data set.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s look at another one.<\/p>\n<p>Find the range of the following set of data:<\/p>\n<div class=\"examplesentence\">{392, 184, 139, 256, 157, 237, and 376}<\/div>\n<p>\n&nbsp;<br \/>\nOur largest value for this set is 392 and our smallest value is 139, so our range is \\(392 \u2013 139\\), which is 253. This is a very large range of data.<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nLet\u2019s try one more example, this time applying it to grades like we did earlier.<\/p>\n<p>A teacher gave five students a test over Mean, Median, Mode, and Range. The scores on the test were: 100, 88, 98, 97, and 83. What is the range of the test grades?<\/p>\n<p>The range is \\(100 \u2013 83\\) which equals 17. The range is low and the test grades are high, so everyone did really well on the test!<\/p>\n<p>I hope this review of statistical range was helpful. Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Statistical_Range_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Statistical Range Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFind the range of the following set of data:<\/p>\n<div class=\"yellow-math-quote\">11, 64, 39, 4, 42, 28, 7, 9<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">2<\/div><div class=\"PQ\"  id=\"PQ-1-2\">55<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">60<\/div><div class=\"PQ\"  id=\"PQ-1-4\">57<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the range, identify the highest value and the lowest value in the data set. The highest value is 64, and the lowest value is 4. Since the range is equal to the difference between these two numbers, subtract to find the range.<\/p>\n<p style=\"text-align: center\">\\(64-4=60\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFind the range of the following set of data:<\/p>\n<div class=\"yellow-math-quote\">564, 329, 463, 442, 570, 389, 451<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">241<\/div><div class=\"PQ\"  id=\"PQ-2-2\">113<\/div><div class=\"PQ\"  id=\"PQ-2-3\">250<\/div><div class=\"PQ\"  id=\"PQ-2-4\">235<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, identify the highest value and the lowest value in the data set. The highest value is 570, and the lowest value is 329. Since the range is equal to the difference between these two numbers, subtract to find the range<\/p>\n<p style=\"text-align: center\">\\(570-329=241\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFind the range of the following set of data:<\/p>\n<div class=\"yellow-math-quote\">4.8, 2.25, 9.8, 7.5, 12.50, 11.2<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">6.4<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">10.25<\/div><div class=\"PQ\"  id=\"PQ-3-3\">9.8<\/div><div class=\"PQ\"  id=\"PQ-3-4\">2.25<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, identify the highest value and the lowest value in the data set. The highest value is 12.50, and the lowest value is 2.25. Since the range is equal to the difference between these two numbers, subtract to find the range.<\/p>\n<p style=\"text-align: center\">\\(12.50-2.25=10.25\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nRose took seven math tests over the course of the last grading period. Her scores are shown below. What is the statistical range of these scores? <\/p>\n<div class=\"yellow-math-quote\">90, 72, 85, 89, 92, 95, 78<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">12%<\/div><div class=\"PQ\"  id=\"PQ-4-2\">18%<\/div><div class=\"PQ\"  id=\"PQ-4-3\">20%<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">23%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, identify the highest value and the lowest value in the data set. The highest value is 95 percent, and the lowest value is 72 percent. Since the range is equal to the difference between these two numbers, subtract to find the range.<\/p>\n<p style=\"text-align: center\">\\(95-72=23\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe forecasted high temperatures in Philadelphia, Pennsylvania for the next nine days are listed below. What is the range of these temperatures? <\/p>\n<div class=\"yellow-math-quote\">72, 66, 82, 77, 84, 72, 66, 63, 66<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">21 degrees<\/div><div class=\"PQ\"  id=\"PQ-5-2\">6 degrees<\/div><div class=\"PQ\"  id=\"PQ-5-3\">18 degrees<\/div><div class=\"PQ\"  id=\"PQ-5-4\">14 degrees<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, identify the highest value and the lowest value in the data set. The highest value is 84 degrees, and the lowest value is 63 degrees. Since the range is equal to the difference between these two numbers, subtract to find the range.<\/p>\n<p style=\"text-align: center\">\\(84-63=21\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/statistics\/\">Return to Statistics Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Statistics Videos<\/p>\n","protected":false},"author":1,"featured_media":100756,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-61997","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-pre-algebra-statistical-analysis-videos","7":"page_category-statistics-videos","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/61997","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=61997"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/61997\/revisions"}],"predecessor-version":[{"id":280496,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/61997\/revisions\/280496"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100756"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=61997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}