Enter the values and weights into the calculator to determine the weighted mean. This calculator can also evaluate any of the variables given the others are known.
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Weighted Mean Formula
The following formula is used to calculate the weighted mean.
WM = Σ(wi * xi) / Σwi
Variables:
- WM is the weighted mean
- wi is the weight of the ith element
- xi is the value of the ith element
To calculate the weighted mean, multiply each value (xi) by its corresponding weight (wi). Sum up all these products. Then, sum up all the weights (wi). Finally, divide the sum of the products by the sum of the weights.
What is a Weighted Mean?
A weighted mean, also known as a weighted average, is a method of calculating an average where some values contribute more than others. In a standard mean, all values are treated equally and contribute the same amount to the final average. However, in a weighted mean, each value is multiplied by a given weight before the average is calculated. The weights are usually represented as a percentage of the total, and the sum of all weights should equal 1 or 100%. This method is often used when some values are considered more important or relevant than others.
How to Calculate Weighted Mean?
The following steps outline how to calculate the Weighted Mean using the given formula:
- First, determine the weight (wi) for each element (xi) in the dataset.
- Next, multiply each element (xi) by its corresponding weight (wi).
- Next, sum up all the products obtained in the previous step.
- Finally, divide the sum of the products by the sum of the weights (Σwi).
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Weighted mean (WM) = ?
Weight (wi) = [0.2, 0.3, 0.5]
Value (xi) = [10, 15, 20]
