In these lessons, we will learn how to solve weighted average problems.
Mean, Median, Mode, Range
Other Algebra Word Problems
There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean), Weighted Average and Average Speed.
The following table gives the formulas for average problems: Weighted Average, Mean, and Average Speed. Scroll down the page for examples and solutions.
One type of average problems 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:
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?
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.
Example of how to calculate the weighted average
At a health club, 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?
How to find the weighted average given a frequency table?
A group of people were surveyed for how many movies they see in a week. The table below shows the result of the survey.
(a) How many people took part in the survey?
(b) What was the total number of movies seen in a week by all the survey takers?
(c) What was the average number of movies seen in a week per person surveyed?
How to solve Weighted Averages and Mixture Problems?
Mixture problems are problems in which two or more parts are combined into a whole.
How to solve Weighted Average Word Problems?
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