Weighted Average Calculator

How to Calculate Weighted Average

A weighted average is a type of average where each value in the data set carries a specific weight. This method is used when certain values are more important or relevant than others in the calculation.

Formula and Its Meaning

The formula for weighted average is:

\[Weighted Average = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}\]

Where:

• \(x_i\) are the individual values in a dataset
• \(w_i\) are the corresponding weights for each value
• \(n\) is the total number of values/weights

Calculation Steps

1. Multiply each value by its corresponding weight.
2. Sum all the products from step 1.
3. Sum all the weights.
4. Divide the sum of products by the sum of weights.

Example Calculation

Let's calculate the weighted average for the following data set:

Values: 85, 90, 95

Weights: 0.3, 0.3, 0.4

1. Multiply each value by its weight:
   85 × 0.3 = 25.5
   90 × 0.3 = 27
   95 × 0.4 = 38
2. Sum the products:
   25.5 + 27 + 38 = 90.5
3. Sum the weights:
   0.3 + 0.3 + 0.4 = 1
4. Divide the sum of products by the sum of weights:
   90.5 ÷ 1 = 90.5

The weighted average is 90.5.

Visual Representation

This diagram illustrates the weighted average calculation for the example. Each blue circle represents a data point, with its size indicating the weight. The vertical position shows the value, and the red line represents the calculated weighted average of 90.5.