Examples of Weighted AveragesDate: 03/26/2001 at 17:27:10 From: Robert Subject: Statistics Can you tell me what is meant by "weighted average," and give me some examples of when and how weighted averages are used? When should mean average be used, versus weighted average? Date: 03/27/2001 at 12:55:56 From: Doctor TWE Subject: Re: Statistics Hi Robert - thanks for writing to Dr. Math. A weighted average is one in which different data in the data set are given different "weights." Here are a few examples: Slugging average in baseball: A batter's slugging average (also called slugging percentage) is computed by: SLG = (1*SI + 2*DO + 3*TR + 4*HR) / AB where: SLG = slugging percentage SI = number of singles DO = number of doubles TR = number of triples HR = number of home runs AB = total number of at-bats Here, each single has a "weight" of 1, each double has a "weight" of 2, etc. The average counts home runs four times as important as singles, and so on. An at-bat without a hit has a "weight" of zero! Slugging average is sometimes referred to as slugging percentage. The term is a misnomer, for it is actually a weighted average, not a percentage. As such, it's possible for a batter's slugging average to exceed 1.000 or 100%. Course grades: Many teachers will use a "weighted average" when calculating a student's grade in a course. For example, a teacher might say the test average is 60% of the grade, quiz average is 30% of the grade, and a project is 10% of the grade. Suppose Mary got 90 and 78 on the tests; 100, 100 and 85 on the quizzes; and an 81 on the project. Her course grade would be: Test average = (90 + 78)/ 2 = 84 Quiz average = (100 + 100 + 85)/3 = 95 Course grade = .60*84 + .30*95 + .10*81 = 87 Here, the tests carry a "weight" of .60 (or .30 each), the quizzes carry a "weight" of .30 (or .10 each), and the project carries a weight of .10. Note that the test average and the quiz average are not weighted averages, but the course grade is. Grade point average (GPA): Most colleges assign "weights" to the individual course grades in the form of credits. A grade in a 4-credit course affects your GPA more by 33% than a grade in a 3-credit course. For example, suppose Joe took the following courses: COURSE CR GR Calculus 4 C Discr. Math 3 A English Lit. 3 A Chemistry 4 D Comp. Sci. 3 B Most colleges use the scale: A = 4, B = 3, C = 2, D = 1, F = 0. To compute Joe's GPA, we multiply each course grade (converted to the number equivalent) by the course credits, then divide the sum by the total number of credits: COURSE CR GR Calculus 4 C 4*2 = 8 Discr. Math 3 A 3*4 = 12 English Lit. 3 A 3*4 = 12 Chemistry 4 D 4*1 = 4 Comp. Sci. 3 B 3*3 = 9 ---- ---- 17 45 GPA = 45 / 17 = 2.65 If the grades had been unweighted, the GPA would have been: (2 + 4 + 4 + 1 + 3) / 5 = 2.80 Why is Joe's GPA lower? Because he did less well in the "more important" courses, i.e. those worth more credits. Here are a few other explanations from our Ask Dr. Math archives that you can check out as well: Weighted Averages http://mathforum.org/dr.math/problems/smith11.2.98.html Calculating a Weighted Average Grade http://mathforum.org/dr.math/problems/sam.5.5.00.html Averaging Averages http://mathforum.org/dr.math/problems/francis.11.9.99.html The term "mean" means average in the conventional sense, in other words, an unweighted average. I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ |
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