wikiHow Practice Problems to Calculate Weighted Average The weighted average is calculated by multiplying each value in a set of data by its corresponding weight, summing the products, and dividing the sum by the total weight. The formula for calculating the weighted average is as follows: Weighted Average = (Value 1 * Weight 1 + Value 2 * Weight 2 + ... + Value n * Weight n) / (Weight 1 + Weight 2 + ... + Weight n) For example, if you have a set of data with three values (10, 20, and 30) and corresponding weights of (2, 3, and 5), the weighted average can be calculated as follows: Weighted Average = (10 * 2 + 20 * 3 + 30 * 5) / (2 + 3 + 5) = (20 + 60 + 150) / 10 = 230 / 10 = 23 Note that the weights should add up to 1 or to a total value that represents 100%. This ensures that the weighted average reflects the relative importance of each value in the data set. Practice Problems: 1. A student has taken three exams with scores of 80, 75, and 90. The exams are equally weighted, with each exam worth 33.33% of the final grade. What is the student's weighted average score? 2. A company has three departments with sales of $100,000, $200,000, and $300,000. The departments have weights of 0.25, 0.5, and 0.25, respectively. What is the weighted average sales of the company? 3. An investor holds three stocks with values of $10, $20, and $30. The weights of the stocks are 0.4, 0.3, and 0.3, respectively. What is the weighted average value of the investor's portfolio? Answer Key: 1. Solution: The formula to calculate the weighted average is (Value 1 * Weight 1 + Value 2 * Weight 2 + ... + Value n * Weight n) / (Weight 1 + Weight 2 + ... + Weight n). Weighted Average = (80 * 0.3333 + 75 * 0.3333 + 90 * 0.3333) / (0.3333 + 0.3333 + 0.3333) = (26.4 + 24.75 + 30) / 3 = 81.15 / 3 = 27.05. The student's weighted average score is 27.05. 2. Solution: The formula to calculate the weighted average is (Value 1 * Weight 1 + Value 2 * Weight 2 + ... + Value n * Weight n) / (Weight 1 + Weight 2 + ... + Weight n). Weighted Average = (100,000 * 0.25 + 200,000 * 0.5 + 300,000 * 0.25) / (0.25 + 0.5 + 0.25) = (25,000 + 100,000 + 75,000) / 1 = 200,000 / 1 = 200,000. The weighted average sales of the company is $200,000. 3. Solution: The formula to calculate the weighted average is (Value 1 * Weight 1 + Value 2 * Weight 2 + ... + Value n * Weight n) / (Weight 1 + Weight 2 + ... + Weight n). Weighted Average = (10 * 0.4 + 20 * 0.3 + 30 * 0.3) / (0.4 + 0.3 + 0.3) = (4 + 6 + 9) / 1 = 19 / 1 = 19. The weighted average value of the investor's portfolio is $19. Page