Question

some teachers use a weighted mean to calculate grades. each score is assigned a weight based on its importance. to find a weighted mean, multiply each score by its weight and add the results. for example, a student’s final chemistry grade is based on four sources: 40% from lab reports, 10% from quizzes, 25% from the midterm exam, and 25% from the final exam. what is the student’s weighted mean given the scores shown in the table? the student’s weighted score is \\(\square\\) (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: List scores and weights

Lab reports: score = 84, weight = 40% = 0.4
Quizzes: score = 90, weight = 10% = 0.1
Midterm exam: score = 76, weight = 25% = 0.25
Final exam: score = 82, weight = 25% = 0.25

Step2: Calculate weighted terms

Lab reports: $84 \times 0.4 = 33.6$
Quizzes: $90 \times 0.1 = 9$
Midterm exam: $76 \times 0.25 = 19$
Final exam: $82 \times 0.25 = 20.5$

Step3: Sum weighted terms

$33.6 + 9 + 19 + 20.5$

Answer:

82.1