Enter a set of data and their weights to instantly compute the weighted average.
Weighted Average Calculate
Result
How to Calculate the Weighted Average
The weighted average (or weighted mean) adjusts the contribution of each data point based on its weight. This is particularly useful when some data points are more important than others. The formula for the weighted average is:
\( \bar{x} = \frac{\sum_{i=1}^{n} (x_i \cdot w_i)}{\sum_{i=1}^{n} w_i} \)
Where:
\( x_i \): The \( i \)-th data point.
\( w_i \): The weight of the \( i \)-th data point.
\( n \): The total number of data points.
\( \sum_{i=1}^{n} (x_i \cdot w_i) \): The sum of all data points multiplied by their weights.
\( \sum_{i=1}^{n} w_i \): The sum of all weights.
Calculation Steps
Multiply Each Data Point by Its Weight: Calculate \( x_i \cdot w_i \) for each data point.
Sum the Weighted Products: Add all the products from Step 1.
Sum the Weights: Add all the weights \( w_i \).
Divide: Divide the sum of the weighted products by the sum of the weights to get the weighted average.
For Example: Data Set = [8, 12, 16, 20], Weights = [4, 3, 2, 1], calculate their weighted average.