Another type of average problem involves the weighted average - which is the average of two or more terms that do not all have the same number of members. To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs.

The formula for weighted average is:

Example:

A class of 25 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class?

Solution:

Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up.

80 × 10 + 60 × 15 = 800 + 900 = 1700

Step 2: Total number of terms = Total number of students = 25

Step 3: Using the formula

Answer: The average score of the whole class is 68.

Be careful! You will get the wrong answer if you add the two average scores and divide the answer by two.

Videos

The following videos give more example of how to calculate the weighted average.

At a health, 80% of the members are men and 20% of the members are women. If the average age of the men is 30 and the average age of the women is 40, what is the average age of all the members?

Find the weighted average given a frequency table

Weighted Average Example

Weighted Averages
How many pounds of mixed nuts selling for $4.75 per pound should be mixed with 10 pounds of dried fruit selling for $5.50 per pound to obtain a trail mix that sells for $4.95 per pound?

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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