Direct answer
A weighted average multiplies every value by its weight, adds those products, and divides by the sum of the weights.
What this calculation tells you
A weighted average summarizes values that do not contribute equally. It reports the centre of the data after each value has been given the influence represented by its quantity, frequency, credit, probability, exposure, or another justified weight.
The result is meaningful only when the weights match the question. Weighting prices by units purchased answers a different question from giving every transaction equal influence.
Where it is used
Education
Combine assignments, examinations, or course results when each component carries different credits or assessment weight.
Finance and investing
Estimate portfolio returns, blended borrowing costs, or average acquisition prices using invested amounts, balances, or quantities as weights.
Operations and inventory
Combine unit costs, production rates, supplier performance, or delivery times across unequal order volumes.
Statistics and research
Summarize observations with different frequencies, sampling representation, or independently justified reliability.
Common situations
- Calculating a course result when the final examination counts more than individual assignments.
- Finding an average purchase price after buying different quantities at different prices.
- Combining regional performance figures without allowing a small region to influence the total as much as a large one.
- Reviewing a blended rate across loans or accounts with different outstanding balances.
When weights matter
An ordinary mean treats every observation equally. A weighted average is appropriate when observations represent different quantities, credits, frequencies, or shares.
The formula is Σ(value × weight) ÷ Σ(weight). If weights already total 100%, the denominator is 100%; otherwise, divide by their actual total.
Worked example
Suppose scores of 70, 80, and 90 have weights of 1, 2, and 3. Their products are 70, 160, and 270. The total is 500 and the weights total 6, so the weighted average is 83.33.
The ordinary mean would be 80, which understates the influence of the highest-weighted score.
Checks before using the result
Confirm that the weights measure the same kind of influence and that a larger weight really should contribute more. Negative weights require a specialized interpretation and are not part of the ordinary weighted-mean workflow.
- Do not sort values without their weights.
- Do not average subgroup averages unless subgroup sizes are used as weights.
- Retain precision until the final displayed result.
What a weighted average can hide
A single weighted result says nothing about how widely the underlying values vary. Two groups can share the same weighted average while one is tightly clustered and the other contains extreme highs and lows. Range, distribution, and subgroup results may therefore matter as much as the headline number.
The choice of weights can also embed a judgment. Credits give more influence to larger courses, transaction volumes favor larger flows, and reliability weights favor observations considered more precise. A result is only meaningful when that interpretation matches the decision being made.
- Show the weight definition beside the result.
- Inspect the underlying values for outliers or distinct groups.
- Do not use weights merely to make the result look more favorable.
Practical questions
Frequently asked questions
Do weighted-average weights have to add to 100%?
No. Relative weights can use credits, units, balances, frequencies, or other non-negative quantities. Dividing by their total normalizes them automatically.
Can I average several subgroup averages?
Only with care. If subgroup sizes differ, use those sizes as weights. Taking an ordinary mean of subgroup averages gives every subgroup equal influence regardless of how many observations it contains.
Does a weighted average describe variability?
No. It provides one measure of location. Review the range, distribution, outliers, and subgroup results when variation affects the decision.