A Weighted Average Calculator is a tool used to calculate the average of a set of data points where each data point contributes a different amount (or “weight”) to the final average. Unlike a simple average, where each data point contributes equally, a weighted average assigns a different level of importance to each data point.

What is a Weighted Average?

A weighted average is calculated by multiplying each data value by its corresponding weight, summing these products, and then dividing by the sum of the weights. This method is particularly useful when different data points should contribute differently to the final result.

The formula for calculating a weighted average is:

$$\bar{x} = \frac{\sum_{i=1}^{n} w_i \cdot x_i}{\sum_{i=1}^{n} w_i}$$

Where:

• $x_i$  is each individual data point.
• $w_i$  is the weight corresponding to each data point.
• $\sum_{i=1}^{n} w_i$  is the sum of all weights.

Steps to Calculate a Weighted Average:

1. Multiply each data value by its corresponding weight.
2. Sum all the weighted data values.
3. Sum all the weights.
4. Divide the sum of weighted data values by the sum of weights.

Example Calculation

Suppose you have the following data:

• Data Values: 50, 60, 70
• Weights: 1, 2, 3

To calculate the weighted average:

1. Multiply each data value by its corresponding weight:

   • $50 \times 1 = 50$ 
   • $60 \times 2 = 120$ 
   • $70 \times 3 = 210$ 

2. Sum the weighted values:

   • $50 + 120 + 210 = 380$ 

3. Sum the weights:

   • $1 + 2 + 3 = 6$ 

4. Divide the sum of weighted values by the sum of weights:

   • $\frac{380}{6} \approx 63.33$
     

So, the weighted average is approximately $63.33$.