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Calculating a Weighted Average
The following table demonstrates how a weighted grade is calculated. The percentage in each category is multiplied by its respective weight. The sum of the results is the total grade percentage.
Category  Percentage in Category  Weight of Category  Result  

Homework  93%  x  .30  0.279 
Quiz/Test  88%  x  .50  0.440 
Exam  91%  x  .20  0.182 
.901  
Total  90.1% 
The question that often arises is "What must I get on the final to bring my grade to a certain level?" Let us represent the above table as an algebraic expression using h, q, ande to represent the categories: homework, quiz/test, and exam respectively. This is done as follows: h*the weight of h + q*the weight of q + e*the weight of e = final grade. To solve for the grade on the exam, enter in the available information with x representing the grade on the final exam and the desired grade for the class. The following is an example.
Category  Percentage in Category  Weight of Category  Result  

Homework  95%  x  .30  0.285 
Quiz/Test  86%  x  .50  0.43 
Exam  ?  x  .20  ? 
Total  90% 
Mathematically this problem can then be solved as follows.
h*(the weight of h) + q*(the weight of q) + e*(the weight of e) = final grade
(.95)*(.30) + (.86)*(.50) + x (.20) = .90
.285 + .43 + .2x = .90
.715 + .2x = .90
.2x = .90  .715
.2x = .185
x = .185/.2
x = .925
92.5%
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