To calculate a weighted average with two weights, you multiply each value by its corresponding weight, and then divide the sum of those products by the sum of the weights.
Here's a breakdown of the process:
1. Identify the values and their corresponding weights:
You'll have two values, let's call them value1 and value2. Each value will have a weight associated with it, weight1 and weight2, respectively. The weight represents the importance or contribution of each value to the overall average.
2. Multiply each value by its weight:
- Calculate value1 * weight1
- Calculate value2 * weight2
3. Sum the products:
Add the results from step 2: (value1 * weight1) + (value2 * weight2)
4. Sum the weights:
Add the two weights: weight1 + weight2
5. Divide the sum of the products by the sum of the weights:
Divide the result from step 3 by the result from step 4:
Weighted Average = [(value1 * weight1) + (value2 * weight2)] / (weight1 + weight2)
Example:
Let's say you have two test scores:
- Test 1: Score = 80, Weight = 60% (or 0.6)
- Test 2: Score = 90, Weight = 40% (or 0.4)
Calculation:
-
Multiply each score by its weight:
- 80 * 0.6 = 48
- 90 * 0.4 = 36
-
Sum the products:
- 48 + 36 = 84
-
Sum the weights:
- 0.6 + 0.4 = 1
-
Divide the sum of the products by the sum of the weights:
- 84 / 1 = 84
Therefore, the weighted average score is 84.
Formula Summary:
Weighted Average = (value1 weight1 + value2 weight2) / (weight1 + weight2)
This formula allows you to accurately calculate the average when different data points have varying degrees of importance.
