An average is a measure of the center of a data set. You calculate the average by adding together all the data points and dividing by the total number of data points. Each number counts equally in the calculation. In a weighted average, some numbers count more than others or carry more weight, so use a weighted average whenever some data points are worth more than others.
When Calculating Grades
Weighted averages are frequently used when calculating a final grade for a specific course, as the final comprehensive exam usually counts more toward the course grade than each of the chapter tests. If you did poorly on the three chapter tests, getting grades of 50 percent, 50 percent and 40 percent but you aced the final at 97 percent, your average will only be 59.25 percent if all the tests counted equally -- the sum of the total scores, 237 divided by the number of tests, 4. If your teacher told you that the final exam was worth as much as the chapter tests, you would assign a weight of 3 to the final and a weight of one to each of the chapter tests. Multiply each test score by its weight, to obtain, 50, 50, 40 and 291. The sum of the weights is 431 divided by the total number of points, 6. Your weighted average would be 71.83 percent, a much higher score.
When Costs Differ
If you are working in manufacturing and you sell products at different costs, you need to use a weighted average because some products are more valuable than others. For example, product A is worth $6.50 and you sell 100 pounds of it, product B is worth $7.95 and you sell 80 pounds of it and product C is worth $14.50 and you sell 60 pounds of it. You would say you are selling products at an average rate of $9.65 because you would sum the dollars to $28.95 and divide by 3, the total number of products. But this average does not take into account cost per pound. Therefore the weighted average should be derived by multiplying the price per unit by the pounds sold. The sum of these three numbers, $2,156.00, is divided by the total number of pounds sold, which is 240. The weighted average is $8.98.
Average Bond Yield
The weighted average is commonly used in financial calculations such as when you want to know the average amount of time left before mortgages in a mortgage-backed security expire. If you have two mortgages in your portfolio, one worth $10,000 expiring in 5 years and one worth $20,000 expiring in 10 years, the average time left before expiration is 7.5 years, but this does not take into account the value of the mortgages -- you have much longer to wait on the mortgage that is worth more. Calculate an average weighted by the worth of each mortgage by taking the value of mortgage one over the total portfolio value or $10,000/$30,000 multiplied by the number of years left or 5. Add this figure to the value of the second mortgage over the total portfolio value, or $20,000/$30,000 multiplied by 10 years. When considering the value of the mortgage, your weighted average would be 8.33 years.
Calculating Batting Average
When calculating batting averages in baseball, a weighted average is typically used, with each type of hit carrying a different weight. A player was at bat a total of 28 times and he struck out 5 times and hit 4 singles, 5 doubles, 6 triples and 8 home runs. Each of these results carries a different weight, a no-hitter=0, a single=1, a double=2, a triple=3 and a home run=4. His weighted batting average is the sum of each of these hits types multiplied by their respective weights, or 64, divided by the total number of times at bat, or 28. This player's weighted batting average is, therefore 2.29.
About the Author
Brenda Scottsdale is a licensed psychologist, a six sigma master black belt and a certified aerobics instructor. She has been writing professionally for more than 15 years in scientific journals, including the "Journal of Criminal Justice and Behavior" and various websites.