Algebra: Average of an Average
Date: 10/20/97 at 18:38:24 From: Ron Cook Subject: Algebra: average of an average Hi! This one is a real-life need. I work for Andersen Consulting and am having a hard time remembering my basic Algebra! If the "Wireless" line of business hires 50 people in one month, and the "Multimedia" line of business hires 80 people in one month, what is the average number of people per month we are hiring? At first, one thinks (50 + 80)/2 = 65 is the correct answer, but it's not because we're taking the average of an average, right? Don't you have to let x = something and then do 1/50 + 1/80 and solve... or something? Please help! Thanks, R. S. Cook
Date: 10/20/97 at 20:25:21 From: Doctor Tom Subject: Re: Algebra: average of an average Hi Ron, 65 is the correct answer if the question is: "What is the average number of people hired per line of work per month?" Assuming that the entire company is made up of only those two lines of business, and you're asking "What is the average number of people hired by the whole company per month?", the answer is obviously 50+80 = 130. The operations above are perfectly reasonable. Let me show you the kind of situation that I think you were worried about, and you'll see why it's different from the situations above: I take 4 exams and have an average score of 80. Then I take 2 more exams and on those 2, my average is 100. What's my overall average for the course? The wrong way to do it is (80+100)/2 = 90. This is wrong because the averages were of different-sized groups. To get the correct answer, I know that on the first 4 exams I got 320 total points because when I divide 320 by 4, I get 80. Similarly, for the last two exams, I must have gotten 200 points total. So for the six exams, I got 200+320 = 520 points and 520/6 = 86.66666 = my real grade average. For your problem, the averages you are averaging are for the same period, so it works out. To convince you that it's true, let's just look at a situation where the averages came from 10 months of data. Then in the first line of business, 500 people must have been hired, since 500/10 = 50. Similarly, 800 were hired in the other, since 800/10 = 80. Altogether, 1300 people were hired in the ten months, or 1300/10 = 130 per month, company-wide. Or if you're trying to get the average per line of work, 65 is right, since if each group had hired 65 people each month for 10 months, there would be 65*20 = 1300 total hires, so it works out. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 10/21/97 at 08:57:12 From: ronald.s.cook Subject: Re: Algebra: average of an average Thanks! You know me better than myself. Ron
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