Weighted Average
CONCEPTS
Weighted Mean / Average
1) Weighted average = (factor a₁ * factor b₁ + factor a₂ * factor b₂) / (factor b₁ + factor b₂)
2) Weighted average = factor a₁ * b₁/(b ₁+ b ₂) + factor a ₂ * b ₂/(b ₁+ b ₂)
3) Weighted average = factor a₁ * % of factor b + factor a ₂ * % of factor b
• The mean or avg problems have the same weight for each number. What if the weights or contributions to the average are different (such as quizzes vs tests)?
Tips
• Think of exams & quizzes. Exams count 20% towards the grade & quizzes count 10%. These are weights.
• There are always 2 variables – 1) factor & 2) weight or contribution factor
• The mean or average problems have the same weight for each number. What if the weights or contributions to the average are different (such as quizzes vs tests)...this is where you used the weighted average equation.
PRACTICE PROBLEMS
Question 1 A student takes 2 tests each worth 40% and 2 quizzes each worth 10%. The scores that the student gets are as follows: tests - 89%, 68% and quizzes - 80%, 95%
-- Answer -- 80.3%
Weighted average = 89% (40%/100%) + 68% (40%/100%) + 80% (10%/100%) + 95% (10%/100%)
Question 2 5 red balls weigh 10 oz, 3 blue balls weigh 5 oz, 2 yellow balls weigh 7 oz. What's the average weight of the balls?
-- Answer -- 7.9
Weighted average (1st equation) = 10 * 5 / 10 + 5 * 3 / 10 + 7 * 2/ 10
Weighted average (2nd equation) = 5 * 10 + 3 * 5 + 2 * 7 / (5 + 3 + 2)
Question 3 What is the mean of the 90 ratings in the histogram below?
-- Answer -- 2.4
Weighted average = 0 * 5/90 + 1 * 10/90 + 25 * 2/90 + 3 * 40/90 + 4 * 10/90 = 220/90 = 2.4
ACT PRACTICE PROBLEMS
