Weighted Average Two Groups
Calculator
Results
- Weighted mean
- 84.8
- Combined size
- 50
Statistical results
| Weighted mean | 84.8 |
| Combined size | 50 |
formula-map diagram
- Weighted mean
- 84.8
- Combined size
- 50
Statistical relationship
Formula
x̄ = (n₁x̄₁ + n₂x̄₂) / (n₁ + n₂)= 84.8
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
How is a weighted average different from a simple average of two numbers?+
A simple average treats both groups equally regardless of their size, while a weighted average accounts for how many items or how much weight each group contributes. Averaging a class of 10 students' average score with a class of 100 students' average score should weight the larger class more heavily.
What is the formula for combining two groups?+
The combined weighted average is (value1 × weight1 + value2 × weight2) / (weight1 + weight2). This ensures each group's contribution to the final average is proportional to its size or weight, not just its value.
Why can't I just average the two group averages directly?+
Averaging two averages directly implicitly assumes both groups are the same size, which is rarely true and produces a biased result when they aren't. This is a classic error known as the 'Simpson's paradox' setup, or more simply, an unweighted average of averages.
What happens if one group's weight is zero?+
If one group has a weight of zero, it contributes nothing to the combined average, and the result equals the other group's value entirely. This makes sense since a weight of zero means that group has no actual presence in the combined data.
Can weights be things other than sample size, like importance or price?+
Yes, weights can represent any meaningful measure of contribution, such as the number of shares in a portfolio return calculation, or credit hours in a GPA calculation. The math is identical regardless of what the weight physically represents, as long as it reflects relative contribution.