# 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*, and*e* 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%Try the Online Grade Calculator »**