Weighted averages, or weighted means, take a series of numbers and assign certain values to them that reflect their significance or importance within the group of numbers. A weighted average may be used to evaluate trends in accounting, investing, grading, population research or other fields in which large quantities of numbers are gathered. The benefit of using a weighted average is that it allows the final average number to reflect the relative importance of each number that is being averaged.
Definition of Weighted Average
In order to determine a weighted average, you must assign a value to each of the numbers that you want to average, and then multiply the value by the respective numbers. Add the total of all of these multiplied values and divide it by the sum of all of the original values. This will yield the weighted average, which takes into account the relative importance of each number in your sample.
Smooth Out Fluctuations
The major benefit of weighted averages for stocks and accounting is that it smoothes out fluctuations in the market. The normal average may be a bad indicator of stock trends, which may have huge fluctuations in a short amount of time. The weighted average takes into account these fluctuations in regard to the amount of time that they spend at a particular price. The weighted average reflects a more long-term and consistent valuation of a stock.
Accounts for Uneven Data
In population studies or census data, certain segments of a population may be over or under represented. Weighted averages take into account the portions that may have uneven representation, and they account for them by making the final product reflect a more balanced and equal interpretation of the data. This type of average is particularly useful in data dealing with demographics and population size.
Assumes Equal Values are Equal
The benefit of the weighted average system is that it assumes that equal values are equivalent in proportion. For example, a teacher might want to determine the relative age of her first graders. She knows that all of the students are 4, 5 or 6 years old. She can count the number of students in each age group, and then take a weighted average to determine the average age of the students. This makes her task simple because she can assume that all children who are five will be accounted for equally and evenly in the final average.