Math

QuestionCalculate your final course average using the weights: Tests (13\%), Labs (10\%), Homework (32\%), Final Exam (45\%). Grades: Tests (75\%), Labs (54\%), Homework (63\%), Final Exam (84\%). What is your weighted average?

Studdy Solution

STEP 1

Assumptions1. The weights for the categories are as follows Tests -32%, Labs -13%, Homework -10%, Final Exam -45% . The grades earned in each category are as follows Tests -75%, Labs -54%, Homework -63%, Final Exam -84%
3. The final grade is a weighted average of the grades in each category

STEP 2

We need to calculate the weighted average. The formula for a weighted average isWeightedAverage=(Grade×Weight)Weighted\, Average = \sum (Grade \times Weight)

STEP 3

First, we need to convert the percentage weights and grades to decimal form. This can be done by dividing each percentage by100.

STEP 4

Convert the weights and grades to decimal form.
Weights32%=0.32,13%=0.13,10%=0.10,45%=0.45Weights32\% =0.32,13\% =0.13,10\% =0.10,45\% =0.45Grades75%=0.75,54%=0.54,63%=0.63,84%=0.84Grades75\% =0.75,54\% =0.54,63\% =0.63,84\% =0.84

STEP 5

Now, we can calculate the weighted average by multiplying each grade by its corresponding weight and then summing the results.
WeightedAverage=(0.75×0.32)+(0.54×0.13)+(0.63×0.10)+(0.84×0.45)Weighted\, Average = (0.75 \times0.32) + (0.54 \times0.13) + (0.63 \times0.10) + (0.84 \times0.45)

STEP 6

Perform the multiplication in each term.
WeightedAverage=0.24+0.0702+0.063+0.378Weighted\, Average =0.24 +0.0702 +0.063 +0.378

STEP 7

Sum the results to get the weighted average.
WeightedAverage=0.24+0.0702+0.063+0.378=0.7512Weighted\, Average =0.24 +0.0702 +0.063 +0.378 =0.7512

STEP 8

Convert the decimal form of the weighted average back to a percentage by multiplying by100.
CourseAverage=0.7512×100Course\, Average =0.7512 \times100

STEP 9

Calculate the course average.
CourseAverage=.7512×100=75.12%Course\, Average =.7512 \times100 =75.12\%The course average is75.12%.

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