{"id":6531,"date":"2016-11-28T06:00:17","date_gmt":"2016-11-28T11:00:17","guid":{"rendered":"http:\/\/grockit.com\/blog\/collegeprep\/?p=2107"},"modified":"2020-09-11T20:42:31","modified_gmt":"2020-09-11T20:42:31","slug":"act-math-averages","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/act\/act-math-averages\/","title":{"rendered":"ACT Math: Averages"},"content":{"rendered":"<p>Averages, or arithmetic means, are likely to show up on the ACT Math section. Most of us know how to find the average, but the test will probably present average questions in a more complicated way.<br \/>\nRather than present you with all the numbers in a set and ask you to find the average of those numbers, the ACT average problems will present you with various combinations of known and unknown information.<br \/>\nBefore we begin, let&#8217;s go over some basic rules for finding averages. There are 3 numbers you want to know; they are related by the formula A= T \/ n, where A is average, T is the total sum of values, and n is the number of figures in a set.<br \/>\n&nbsp;<br \/>\n<div  class='avia-icon-list-container   avia-builder-el-0  el_before_av_heading  avia-builder-el-first '><ul class='avia-icon-list avia-icon-list-left av-iconlist-big avia_animate_when_almost_visible avia-iconlist-animate'>\n<li><div  class='iconlist_icon  avia-font-entypo-fontello'><span class='iconlist-char ' aria-hidden='true' data-av_icon='\ue816' data-av_iconfont='entypo-fontello'><\/span><\/div><article class=\"article-icon-entry \"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='iconlist_content_wrap'><header class=\"entry-content-header\"><h4 class='av_iconlist_title iconlist_title   '  itemprop=\"headline\"  >1. The number of figures in a set (n)<\/h4><\/header><div class='iconlist_content  '  itemprop=\"text\"  ><p>If I want to find the average of seven different test scores, then n=7.<\/p>\n<\/div><\/div><footer class=\"entry-footer\"><\/footer><\/article><div class='iconlist-timeline'><\/div><\/li>\n<li><div  class='iconlist_icon  avia-font-entypo-fontello'><span class='iconlist-char ' aria-hidden='true' data-av_icon='\ue816' data-av_iconfont='entypo-fontello'><\/span><\/div><article class=\"article-icon-entry \"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='iconlist_content_wrap'><header class=\"entry-content-header\"><h4 class='av_iconlist_title iconlist_title   '  itemprop=\"headline\"  >2. The sum total of all the figures in a set (T)<\/h4><\/header><div class='iconlist_content  '  itemprop=\"text\"  ><p>If the aforementioned scores are 80, 60, 70, 80, 95, and 90, 75, then T= 550.<\/p>\n<\/div><\/div><footer class=\"entry-footer\"><\/footer><\/article><div class='iconlist-timeline'><\/div><\/li>\n<li><div  class='iconlist_icon  avia-font-entypo-fontello'><span class='iconlist-char ' aria-hidden='true' data-av_icon='\ue816' data-av_iconfont='entypo-fontello'><\/span><\/div><article class=\"article-icon-entry \"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='iconlist_content_wrap'><header class=\"entry-content-header\"><h4 class='av_iconlist_title iconlist_title   '  itemprop=\"headline\"  >3. The average of the figures in a set: (A)= T \/ N<\/h4><\/header><div class='iconlist_content  '  itemprop=\"text\"  ><p>In our example, A = 550 \/ 7 = 78.57.<br \/>\nThe most important rule to remember is that Average = Sum Total \/ Number of Figures<\/p>\n<\/div><\/div><footer class=\"entry-footer\"><\/footer><\/article><div class='iconlist-timeline'><\/div><\/li>\n<\/ul><\/div><br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-1  el_after_av_iconlist  el_before_av_heading  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Questions and Strategies<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nHere are some possibilities for average questions and the strategies to solve them:<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h4  blockquote modern-quote  avia-builder-el-2  el_after_av_heading  el_before_av_heading  '><h4 class='av-special-heading-tag '  itemprop=\"headline\"  >Finding the total<\/h4><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nIF you know the <strong>average<\/strong> and the number of figures\/items (<strong>n<\/strong>) in a set, then simply multiply the average and the number of figures to find the sum total (<strong>T<\/strong>).<br \/>\n<strong>Example 1<\/strong>: John caught 14 fish after a long day of fishing. After weighing all of them together, he calculated the average weight of the fish to be 4.7 lbs. What is the total weight, in pounds, of all the fish?<br \/>\nAnswer: Simply multiply 14 and 4.7.<br \/>\n14*4.7= 65.8<br \/>\n<strong>Example 2<\/strong>: Throughout the year, Janet took 8 math tests; her average score was 83. If her average score after the first three five tests was 89, what was the average of her last three tests?<br \/>\nHere, we have to find two totals before we can calculate the average of the final three tests.<br \/>\n8*83= 664, the total number of percentage points on all the tests<br \/>\n5*89= 445, the total number of percentage points on the first five tests.<br \/>\nWith this information, we know that the total number of percentage points on the last three tests must be the total of <em>all<\/em> the tests minus the total of the first five tests:<br \/>\n664-445 = 219<br \/>\nNow, we have the info we need to find the average in question.<br \/>\n219 (total) \/ 3 (number of figures) = 73<br \/>\n<strong>Example 3:<\/strong> If the average of 34, 44, 28, and x is 35, what is the value of x?<br \/>\nRemember that Average = Total \/ Number of figures.<br \/>\nAll you have to do is set up an equation with the information you know. Don&#8217;t forget that &#8216;x&#8217; counts as a number in the list, so our total number of figures is 4.<br \/>\n35= ( 34+44+28+x) \/ 4<br \/>\n35= 106 + x \/ 4<br \/>\n4 (35) = 106 + x<br \/>\nx = 4(35) &#8211; 106<br \/>\nx = 34<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h4  blockquote modern-quote  avia-builder-el-3  el_after_av_heading  avia-builder-el-last  '><h4 class='av-special-heading-tag '  itemprop=\"headline\"  >Average Speed = total distance \/ total time<\/h4><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe formula for average speed is quite simple and intuitive, but many overlook the formula when approaching average speed problems. Remember, we need both the total distance and the total time to calculate average speed.<br \/>\n<strong>Example 4<\/strong>: In traveling from city A to city B, John drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was his average speed for the whole trip?<br \/>\nFirst, let&#8217;s figure out the total distance. 1 hour at 50 mph would be 50 miles, and 3 hours at 60 mph would be 180 miles. Our total distance is 180 + 50 = 230 miles. The total time is 3+1 = 4 hours.<br \/>\nAverage Speed = total distance \/ total time = 230 \/ 4 = 57.5<br \/>\nNote: the average speed is not merely the average of 50 and 60&#8211;that is a mistake that many students make. If John traveled a greater distance at 60 mph, it wouldn&#8217;t make sense for the average speed to lie right in the middle of 50 and 60. Rather, the average speed should be closer to 60.<br \/>\nAlways remember: when in doubt, go back to the formula A=T \/ n. Even the most complicated average problems stem from the formula.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Averages, or arithmetic means, are likely to show up on the ACT Math section. Most of us know how to find the average, but the test will probably present average questions in a more complicated way. Rather than present you with all the numbers in a set and ask you to find the average of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27029,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[58],"tags":[792],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6531"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=6531"}],"version-history":[{"count":3,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6531\/revisions"}],"predecessor-version":[{"id":36126,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6531\/revisions\/36126"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27029"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=6531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=6531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=6531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}