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Averages & Weighted Averages

A simple average treats all values equally. A weighted average gives more importance to some values than others.

Practice This Concept

Understanding 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

$\bar{x}_w = \frac{\sum(v_i \times w_i)}{\sum w_i}$

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

1
(4.5 + 7.3) ÷ 2 = 5.9

Simple average of France and Germany CO2

2
(4.5×67 + 7.3×83) ÷ (67+83) = 6.05

Weighted average — Germany counts more (bigger population)

3
(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.

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