Calculate Weighted Average
A weighted average is a more accurate measurement of scores or investments that are of relative importance to each other. This is often the case with investment portfolios, grade scoring and other statistics. You can find out how to calculate weighted averages.
Contents
Steps
Preparation
- Sit down with your data, a piece of paper and a pencil. You may need to read a report or story problem to recognize the numbers and their weights before doing the problem.
- Grab a calculator. It is usually faster to multiply percentages with a calculator.
Identify Values
- Identify the numbers that are weighted. You may want to write them down on your paper in a chart form.
- For example, if you are trying to figure out a grade, you should identify what you were graded on each exam.
- Identify the weights of each number. This is often a percentage. List the weight next to the number.
- Percentages are common because weights are often a percentage of a total of 100. If you are figuring out the weighted average of grades, investments and other financial data, look for the percentage of the occurrence out of 100.
- If you are figuring the weighted average of grades, you should identify the weight of each exam or project.
- Convert percentages to decimals. Always multiply decimals by decimals, instead of decimals by percentages.
Multiply for Weighted Average
- Multiply each number by its weight.
- You can choose to write this at the end of the chart or to do it on 1 line, in a formula. For example, if you are trying to figure out the weighted average of certain grades, you might write 0.9(0.25) to indicate a 90 percent grade times 25 percent of the total grade.
- Add the weighted scores together.
- For example, 0.9(0.25) + 0.75(0.50) + 0.87(0.25). The total weighted score for the class would be 0.8175.
- Note that the weights should total 100 if you are using percentages. Continue reading to adjust the weighted average for different types of weights.
- Multiply by 100 to get the percentage. In our grade example, this is 81.75 percent.
Weighted Averages without Percentages
- Adjust your formula for an answer that does not include percentages.
- Identify a numerical weight for each number value. Multiply the number by the weight, just as you did with percentages.
- Add together the values after you have multiplied them by their weights.
- Add together the weights for each value.
- Divide the total of the values by the total of the weights. The answer is the average value for each number.
Tips
- You can solve for the grade you need to receive on a test by plugging a variable in the weighted averages formula. For example, if you need to find out what grade you need to receive an 80 percent grade in our example above, write 0.9(0.25) + 0.75(0.50) + x(0.25)=0.80. Solve for x. You would need an 80 percent on the test to get an 80 percent in the class.
Warnings
- Weighted average is not the same as the mean. If you took the mean of 90, 75 and 87 percent scores, you would arrive at an answer of 84 percent, an incorrect answer when weights of 25, 50 and 25 percent are to be factored in. The answer should be 81.75 percent.
Things You'll Need
- Calculator
- Pencil
- Paper
- Report/data
- Chart
