Calculating a Grade Average
Date: 08/15/99 at 22:13:58 From: Rachel Subject: Finding my exact average This year my dad wants me to keep track of all my scores of worksheets, tests, etc. to find out what my average is. Well here's my problem: If some things are worth more than others are, how can I do that? Thank you! Rachel
Date: 08/16/99 at 04:42:43 From: Doctor Jeff Subject: Re: Finding my exact average Hello, Rachel. Thanks for writing to Dr. Math. Let's assume that your average is calculated on a point system. That is, everything is worth a certain number of points, and certain things are worth more points than others are. A test might be worth 100 points; a paper, 50 points; and a quiz, 10 points. Here are a student's scores, using the above system, for the first quarter of the school year: Quizzes Papers Tests 9/10 or 90% 43/50 or 86% 79/100 or 79% 7/10 or 70% 41/50 or 82% 92/100 or 92% 10/10 or 100% 90/100 or 90% 8/10 or 80% 8/10 or 80% If you want to calculate the student's average for the entire first quarter, the easiest way is to add up the total number of points the student earned and divide that by the total number of points the student could have earned. In this case, it's best to avoid dealing with the individual percentages, since, for example, a 90% score on a quiz does not count nearly as much as a 90% on a test. This student's average would then be: 9+ 7+10+ 8+ 8+43+41+ 79+ 92+ 90 387 -------------------------------- = --- = .86 = 86% 10+10+10+10+10+50+50+100+100+100 450 Of course, not all teachers use this simplified point system. Perhaps a more common method for determining a student's average goes something like this: "Quizzes are worth 20% of your grade; homework is worth another 10%; papers are worth 30%; the final is worth 30%; and class participation is worth the remaining 10%." In this scenario, students might only be given percentages for their work. Let's say a student received the following scores: Quizzes Homework Papers Final Participation 95% 84% 85% 88% 100% 80% 100% 89% 75% 100% 90% 90% 91% The first thing the student needs to do is come up with an average for each of the five categories above. Let's assume that each quiz is worth the same as every other quiz, that each homework assignment is worth the same as every other homework assignment, etc. To find an average for a category, simply add up the percentages and divide by the number of scores there are. For example, the quiz average would be: 95%+80%+75%+90% 340% --------------- = ---- = 85% 4 4 The category averages are: Quizzes = 85% Homework = 93% Papers = 87% Final = 88% Partic. = 100% Now, remembering that each category is worth a certain amount in calculating the average for the quarter, multiply the average for each category by the fraction of the quarter average that the category represents: Quizzes: 85% * .2 = 17% Homework: 93% * .1 = 9.3% Papers: 87% * .3 = 26.1% Final: 88% * .3 = 26.4% Partic.: 100% * .1 = 10% Now, just add up these new percents to get the student's weighted average for the entire quarter: 17% + 9.3% + 26.1% + 26.4% + 10% = 88.8% Related to this question of calculating averages is how to determine what a student needs to score on, say, a test, to get a certain grade. Let's pretend that our student has not yet taken her final. The question is, assuming the student has the rest of the grades listed above, what does she need to get on the final to raise her average to a 90%? We already saw that summing the products of each category's percent and its "category worth" will give us a student's average. We can use this same equation, but this time call the first quarter's average 90%, since that's what the student is aiming for. Then all we need do is solve for the grade on the final, which we'll call f for simplicity: average = 90% = 17% + 9.3% + 26.1% + (.3*f) + 10% 90% = 62.4% + (.3*f) 27.6% = .3*f 92% = f The student must, therefore, score at least 92% on the final to raise her average to the 90% level. There are about as many ways of calculating averages as there are teachers. At the beginning of the school year, make sure to find out how your teachers go about their calculations so you don't wind up with completely different grades when report cards are given out! I hope this helped you out. Please write back if you find anything confusing or if you have more questions. - Doctor Jeff, The Math Forum http://mathforum.org/dr.math/
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