Calculating Weighted Average

Definition

• A weighted average is a mean where each number in the dataset is multiplied by a predetermined weight before the final calculation.

Example

• Consider calculating the weighted average of grades in a class:
  • Quizzes: 82
  • Exams: 90
  • Term Paper: 76
• Weights for each component:
  • Quizzes: 20%
  • Exams: 35%
  • Term Paper: 45%

Steps to Calculate

1. Determine Weights

   • Convert percentage weights into decimals:
     • Quizzes: 20% -> 0.2
     • Exams: 35% -> 0.35
     • Term Paper: 45% -> 0.45

2. Multiply Each Grade by its Weighting Factor

   • Quizzes: 82 * 0.2 = 16.4
   • Exams: 90 * 0.35 = 31.5
   • Term Paper: 76 * 0.45 = 34.2

3. Sum the Weighted Grades

   • Total = 16.4 + 31.5 + 34.2 = 82.1*

Result

• The weighted average of the grades is 82.1%.

Key Points

• Weights should be converted to decimals by moving the decimal point two places to the left.
• Each grade is multiplied by its respective weighting factor.
• The products of these multiplications are added together to get the weighted average.