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.
When this guide helps
- 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.
Worked case: assessment weights
A course has an 80 score worth 40% and a 90 score worth 60%.
Multiply before adding: 80 x 0.40 = 32 and 90 x 0.60 = 54. The contributions sum to 86.
The weighted course result is 86, not the unweighted mean of 85.
The 90 score influences the result more because its declared weight is larger.
Reproduce this worked caseOpen Weighted Average Calculator
Worked case: combine quantities bought at different prices
Ten units cost 4 each and thirty units cost 6 each. The useful average price must be weighted by unit count.
Total cost is 10 x 4 + 30 x 6 = 220. Divide by 40 units to obtain 5.50 per unit.
The quantity-weighted price is 5.50, whereas averaging 4 and 6 directly would give 5 and understate the larger purchase.
Weights can be counts, credits, time or another exposure, but they must match the question.
Reproduce this worked caseOpen Weighted Average Calculator
Compare weighted averages cases before generalising
Normalize weights when they do not already sum to one. Do not average subgroup averages without their subgroup sizes, and do not mix weights that represent incompatible exposures.
| Case | Values and weights | Weighted result |
|---|---|---|
| Course | 80 at 40%; 90 at 60% | 86 |
| Purchase | 10 at 4; 30 at 6 | 5.50 |
| Equal weights | 80 and 90 | 85 |
weighted averages: calculation checklist
- Name what each weight represents
- Use value-weight pairs
- Divide by total weight
- Keep zero-weight rows explicit
- Check the result lies within the input range when weights are nonnegative
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.
Further reading
Authoritative sources
Use these primary and professional resources to check definitions, conventions, or requirements that may extend beyond this guide.