Weighted Mean A student of the author earned grades of 63, 91,...

Question

Weighted Mean A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.

Accepted Answer

Welcome back, everyone. A student received the following scores in a mathematics course 72, 85, 91, 78, and 88 on five quizzes. She also scored 89 on the midterm exam, 93 on a group project, and 75 on assignments. The final grade is determined by the following weight distribution quizzes are 50%, midterm exam is 20%, the project is 15%, and assignments are 15%. What is the student's weighted mean score? What letter grade did she earn an A, B, C, D, or F and assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on. A says her weighted mean is 90.2, which corresponds to an A. B says it's 84.4, which corresponds to a B. C 78.9, which corresponds to a C and a D 69.5, which corresponds to a D. Now, how do we compute our final grade? How do we get that weighted mean score? Well, our problem tells us, OK? So now, from our problem statement, we know that the final grade. OK, the final grid, which is gonna be X bar. Is equal to The quiz mean, OK, so it's gonna be the quiz mean multiplied by its weight or the weighted quiz mean. OK. Or rather, let's actually write the weight. So it's gonna be 50% multiplied by the quiz mean. OK. Plus The weight of the midterm, OK. So the weight of the midterm is 20% multiplied by the midterm grade, OK. Plus, the project weight, which is 15% multiplied by the project grade, OK. Plus the assignment with 15% multiplied by that grade, OK. That's all we'll get the final grade. That's what our problem tells us. No, we already know that so far we have our midterm grade, we have our project grade, and we have our assignment grade. So no, we need to figure out the quiz mean so that we can put it into our formula to get the final grade. How can we get the quiz mean? Well, all we need to do is to find the mean of those 5 values for our quiz scores, OK? So we're gonna add those up and divide by 5. So the quiz mean would be 72 + 85 + 91 + 78 + 88, all divided by 5. The sum of those values is 414 and 414 divided by 5 is equal to 82.8. Thus, 82.8 is the quiz mean. Now that we have that value, we can find the final grid because this no implies then that the final grid is going to be equal to 50% or 0.5% multiplied by 82.8. Plus 20% or 0.2 multiplied by 8 to 9 or midterm grade. Plus 15% or 0.15 multiplied by our project grade 93, plus 15% 0.15 multiplied by the assignment grade 75. No, 0.5 multiplied by 82.8 is 4141.4, 0.2 multiplied by 89 is 17.8. 0.15 multiplied by 93 is 13.95 and multiplied by 75, it's 11.25. And when we add all of these up, then we get our final grade to be 84.4. Now remember that we were told a mean of 80 to 89 is a B. Therefore, that means our student or the student earns, the student with her weighted mean of 84.4 earns a B. Thus, B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Weighted Mean

Percentage Weights

Grading Scale

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