Weighted Average

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An average in which each value contributes according to its weight, not equally.

The weighted average of values x_1, x_2, ..., x_n with weights w_1, w_2, ..., w_n is defined as x̄ = Σ(w_i · x_i) / Σ w_i. When all weights are equal, the weighted average reduces to the ordinary arithmetic mean. Weighted averages are the correct tool whenever values carry different importance, sample sizes, or frequencies — for example, combining test scores from classes of different sizes, or computing a GPA where each course counts for a given number of credits.

x̄ = Σ(w_i · x_i) / Σ w_i

• Test scores: class A avg 80 (20 students), class B avg 70 (30 students) → weighted avg = (20·80 + 30·70) / 50 = 74
• GPA: A (3 credits), B (4 credits), C (2 credits) → weighted avg uses credits as weights
• Portfolio return: investments weighted by dollar amount invested

How to recognize it

• Values carry different sample sizes, importance, or frequencies
• Keywords: 'weighted', 'by credits', 'weighted by', 'per unit'
• Equal weights → ordinary mean; unequal weights → weighted mean

Common mistakes

• Taking a plain mean when values have different weights
• Forgetting to divide by the sum of weights
• Using counts and values in the wrong positions

Practice guidance

Numerical Reasoning