{"id":87,"date":"2014-01-15t09:00:34","date_gmt":"2014-01-15t09:00:34","guid":{"rendered":"\/\/www.catharsisit.com\/act\/?p=87"},"modified":"2017-09-28t08:57:30","modified_gmt":"2017-09-28t15:57:30","slug":"the-mathematical-mean-vs-average-speed-on-act-math","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/","title":{"rendered":"the mathematical mean vs. average speed on act math"},"content":{"rendered":"

not all averages are created equal on the act math test<\/a>. what can be somewhat confusing is that the word \u201caverage\u201d on the act math can refer to two separate concepts: the arithmetic mean, and the average speed. it\u2019s important not to confuse the two on the test day, as they require different formulas to solve! here\u2019s what you need to know to tell these two apart!<\/p>\n

the \u201carithmetic mean\u201d is what you\u2019ve probably learned in your high school algebra class as the mathematical average. this is defined as the sum of the terms divided by the number of terms. mean = (sum) \/ (# of terms)<\/b>. for a list of consecutive integers or evenly spaced numbers, the mean is equal to the median, or the middle number. for example, the \u201caverage\u201d of 3, 5, and 9 is 5.67. this is the most-common \u201caverage\u201d and the easier of the two concepts.<\/p>\n

the concept of \u201caverage speed\u201d is often found in complex word problems. this type of question is one many students are less familiar with so you may not have seen it before (and that\u2019s ok). let’s review two important equations to remember and look at how this concept appears on the tough act word problems.<\/p>\n

the first formula to memorize is: d = r x t<\/b>. this stands for distance = rate x time (referred to as the \u201cdirt\u201d formula). it is perfectly acceptable to also think of it as time = distance \/ rate or as rate = distance \/ time as well. usually the \u201crate\u201d is speed but it could be anything \u201cper\u201d anything. in a word problem, if you see the word \u201cper\u201d you know this is a question involving rates.<\/p>\n

the second formula is: average rate = total distance \/ total time<\/b>. this is its own special concept and you will notice that it is not a simple average of the speeds (which would be something like the sum of the speeds \/ the number of different speeds or what we know as the arithmetic mean). average rate is a completely different concept, so do not let the common word \u201caverage\u201d confuse you. this concept is extremely rare on the act math section, but it\u2019s nice to know the formula in case it comes up!<\/p>\n

let\u2019s look at a challenging sample question:<\/p>\n

the average (arithmetic mean) of four numbers is 30. when one of the numbers is removed, the average of the remaining three numbers is 10. \u00a0what number was removed?
\n(a) 30
\n(b) 45
\n(c) 60
\n(d) 75
\n(e) 90<\/p>\n

we know that the four original numbers sum to 30*4 = 120.\u00a0\u00a0the new equation becomes:<\/p>\n

\"4*30<\/p>\n

\"120<\/p>\n

120 – x<\/i> = 30\u00a0 (add an x<\/i> to each side and subtract a 30)
\n90 = x<\/i><\/p>\n

the correct answer is (e).<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

not all averages are created equal on the act math test. what can be somewhat confusing is that the word \u201caverage\u201d on the act math can refer to two separate concepts: the arithmetic mean, and the average speed. it\u2019s important not to confuse the two on the test day, as they require different formulas to […]<\/p>\n","protected":false},"author":97,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[9,6],"ppma_author":[24879],"acf":[],"yoast_head":"\nthe mathematical mean vs. average speed on act math - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"the mathematical mean vs. average speed on act math\" \/>\n<meta property=\"og:description\" content=\"not all averages are created equal on the act math test. what can be somewhat confusing is that the word \u201caverage\u201d on the act math can refer to two separate concepts: the arithmetic mean, and the average speed. it\u2019s important not to confuse the two on the test day, as they require different formulas to […]\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2014-01-15t09:00:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28t15:57:30+00:00\" \/>\n<meta name=\"author\" content=\"magoosh act\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:site\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:label1\" content=\"written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"magoosh act\" \/>\n\t<meta name=\"twitter:label2\" content=\"est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"article\",\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/#article\",\"ispartof\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\"},\"author\":{\"name\":\"magoosh act\",\"@id\":\"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/90c61bb62ffbc6c5d106b40d967ba3a9\"},\"headline\":\"the mathematical mean vs. average speed on act math\",\"datepublished\":\"2014-01-15t09:00:34+00:00\",\"datemodified\":\"2017-09-28t15:57:30+00:00\",\"mainentityofpage\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\"},\"wordcount\":458,\"commentcount\":0,\"publisher\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/#organization\"},\"keywords\":[\"act math test\",\"act strategies\"],\"articlesection\":[\"act\"],\"inlanguage\":\"en-us\",\"potentialaction\":[{\"@type\":\"commentaction\",\"name\":\"comment\",\"target\":[\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/#respond\"]}]},{\"@type\":\"webpage\",\"@id\":\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\",\"url\":\"\/\/www.catharsisit.com\/hs\/act\/the-mathematical-mean-vs-average-speed-on-act-math\/\",\"name\":\"the mathematical mean vs. average speed on act math - 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