Averages & Weighted Averages
A simple average treats all values equally. A weighted average gives more importance to some values than others.
Practice This ConceptUnderstanding Averages & Weighted Averages
The simple average adds all values and divides by how many there are. But when values have different "importance" (like countries with different populations), a weighted average is needed. Each value is multiplied by its weight before averaging. In EPSO, this appears when combining per-capita data across countries of different sizes.
Formula
Key Rules
- Simple average: add all values, divide by count
- Weighted average: multiply each value by its weight, add up, divide by total weight
- Bigger weights pull the average towards their value
- If all weights are equal, weighted average = simple average
- The weighted average is always between the smallest and largest value
Examples in Action
(4.5 + 7.3) ÷ 2
=
5.9
Simple average of France and Germany CO2
(4.5×67 + 7.3×83) ÷ (67+83)
=
6.05
Weighted average — Germany counts more (bigger population)
(10×100 + 20×300) ÷ 400
=
17.5
Weighted avg pulled towards 20 because it has 3× the weight
Common Errors
- Using simple average when the question requires weighted (ignoring population/size differences)
- Multiplying by wrong weights (using GDP instead of population, or vice versa)
- Adding values without multiplying by weights first
Pro Tip
Ask: "should bigger countries count more?" If yes → weighted average. If the question just says "average" with no context → probably simple.