Interactive tool

Weighted Mean Calculator - Values, Weights, Formula, and Examples

Weighted mean is the correct average when each value does not count equally. Formula: weighted mean = sum(value x weight) / sum(weight). Use it for course grades with different credit weights, portfolio returns with different capital allocations, survey results with sample weights, and prices with different quantities. This calculator returns weighted mean, arithmetic mean, total weight, and weighted sum so you can see how much the weights changed the result.

Client-side

Unequal-importance average

Before you calculate

Best forCourse grades, portfolio returns, weighted survey ratings, blended prices, quality scores, inventory costs, and any dataset where one observation should count more than another. InputTwo to 30 values and the same number of positive weights. Weights can be percentages, counts, credits, quantities, hours, dollars, or shares. OutputWeighted mean, arithmetic mean comparison, total weight, weighted sum, and step-by-step products for each value-weight pair.

Three checks that make a weighted mean trustworthy

Weighted mean is simple, but it is only meaningful when the weights represent the real question being asked.

Pairing

Every value must pair with exactly one weight

The first weight belongs to the first value, the second weight belongs to the second value, and so on. If a row is missing its weight, the result is not a weighted average; it is an accidental formula.

Meaning

Weights should measure influence, not preference

Good weights come from credit hours, capital invested, sample size, units sold, or agreed grading percentages. A rank such as 1st, 2nd, 3rd is not automatically a weight unless you have defined what those numbers mean.

Scale

Scaling all weights equally does not change the result

Weights 0.30, 0.25, 0.20, 0.25 and 30, 25, 20, 25 produce the same weighted mean. The danger is mixing scales inside one calculation, such as 30, 0.25, 20, 0.25.

Where weighted mean is the right calculation

Use this table to decide whether your weights represent the real size, importance, or exposure behind each value.

Situation	Input	Best next move	Why
Course grade	Scores 88, 92, 76, 95; weights 30%, 25%, 20%, 25%	Use weighted mean -> 88.35	The final grade must follow the grading policy, not the unweighted average of categories.
Portfolio return	Returns 6%, 12%, -4%, 9%; capital 4000, 2500, 1500, 2000	Weight each return by capital invested	A larger position changes total portfolio return more than a smaller position.
Survey rating	Ratings 5, 4, 3, 2, 1; response counts 120, 240, 180, 90, 30	Use counts as weights	Each rating level represents a different number of respondents.
Equal observations	Values 10, 20, 30; weights 1, 1, 1	Weighted mean = arithmetic mean = 20	When all weights are equal, weighting adds no extra information.

Step-by-step: how to use this calculator correctly

Confirm every value has a matching weight. If you have 5 values, you must enter 5 weights in the same order.

Use weights that describe real importance: credits, quantities, dollars invested, survey counts, or percentage share.

Multiply each value by its matching weight, then add those products to get the weighted sum.

Add the weights separately. The total must be greater than zero, and weights should be positive for this calculator.

Divide weighted sum by total weight. Compare with arithmetic mean to see how strongly the weights changed the average.

Course grade with assignments, quizzes, project, and final exam

Given

Scores: 88, 92, 76, 95 | Weights: 30%, 25%, 20%, 25%

Work

Weighted sum = 88x0.30 + 92x0.25 + 76x0.20 + 95x0.25 = 88.35. Total weight = 1.00.

Result

Weighted mean = 88.35. Arithmetic mean = 87.75, so the heavier final exam and assignment weights raise the grade by 0.60 points.

Takeaway

The weighted mean answers the grading question; the arithmetic mean ignores the course policy and treats every category as equally important.

Weighted mean versus other averages: when equal treatment is wrong

Weighted mean is the right summary when rows do not carry equal importance. The table shows how it differs from arithmetic, geometric, and harmonic mean.

Method	Best for	Watch for	Example
Weighted mean	Values with unequal importance: grade categories, portfolio weights, survey weights, inventory quantities, and blended prices.	Each value needs a matching positive weight. Mixing 30 with 0.25 as if both were percentages is a common scale error.	Scores 88, 92, 76, 95 with weights 30%, 25%, 20%, 25% -> weighted mean = 88.35.
Arithmetic mean	Equal-weight values where every observation counts once.	Wrong when one row represents more credit, money, quantity, time, or survey population than another.	The same scores without weights -> AM = 87.75, which ignores the course grading policy.
Geometric mean	Multiplicative values: growth factors, return indexes, fold changes, and ratios.	Not a substitute for weights. Use GM when values multiply; use weighted mean when values have unequal importance.	Return factors 1.06, 0.92, 1.15 -> GM = 1.038, or 3.8% per period.
Harmonic mean	Rates over equal denominators, such as equal-distance speed or equal-dollar unit cost.	If denominators are unequal, use a weighted approach with the real denominator as the weight.	30 mph and 60 mph over equal distance -> HM = 40 mph.

Grade example: larger weights pull the final average toward the heavier categories

The arithmetic mean of 88, 92, 76, 95 is 87.75. Applying weights 30%, 25%, 20%, 25% gives 88.35 because the stronger categories carry more influence.

Assign

Quiz

Project

Final

87.75

88.35

Weighted mean calculation flow: pair, multiply, sum, divide

The formula is sum(w_i * x_i) / sum(w_i). The denominator normalizes the weights, so they do not need to add to 1 or 100.

01 Pair

Match each value with its weight: 88 with 0.30, 92 with 0.25, 76 with 0.20, 95 with 0.25.

02 Multiply

Compute value x weight for each row: 26.4, 23.0, 15.2, 23.75.

03 Sum

Weighted sum = 26.4 + 23.0 + 15.2 + 23.75 = 88.35. Total weight = 1.00.

04 Divide

Weighted mean = 88.35 / 1.00 = 88.35.

Key facts before you calculate

When weighted mean is the right average

Use weighted mean when observations do not represent equal amounts of evidence. A 4-credit course should affect GPA more than a 1-credit lab. A portfolio position worth $10,000 should affect portfolio return more than a position worth $500. A survey answer from a sampled group may need a population weight. In each case, arithmetic mean answers the wrong question because it gives every row the same influence.

Weights can be percentages, counts, or quantities

Weights only need to be proportional. Grade weights of 30, 25, 20, 25 produce the same weighted mean as 0.30, 0.25, 0.20, 0.25 because both sets have the same relative importance. Do not mix scales in one calculation, such as using 30 for one percentage and 0.25 for another. Convert all weights to the same scale first.

Use arithmetic mean only when every value counts equally

If each observation has the same importance, weighted mean collapses to arithmetic mean. Example: values 10, 20, 30 with weights 1, 1, 1 give weighted mean = 20, the same as AM. The moment weights differ, the weighted mean moves toward the values with larger weights.

Weighted mean mistakes that quietly change the answer

Most weighted-average errors do not break the formula. They produce a neat-looking number that answers the wrong question.

Watch for

Entering values and weights in different orders

Keep the order identical. If 95 is the final exam score, its weight must sit in the same position as the final exam weight.

Watch for

Mixing percentage scales

Use either 30, 25, 20, 25 or 0.30, 0.25, 0.20, 0.25. Do not mix whole percentages and decimals in the same weight list.

Watch for

Using weights that do not represent the question

A weight should describe importance, quantity, exposure, or sample size. If the weights are arbitrary, the weighted mean is arbitrary too.

Keep going

Related calculators and reference guides

Continue with the Statistics hub, compare this result against a related method, or open a guide that covers the same data pattern in more depth.

HubStatistics Calculators: Arithmetic, Weighted, Geometric, and Harmonic Mean

The three Pythagorean means — arithmetic, geometric, and harmonic — each answer a different averaging question. Arithmetic mean sums values; geometric mean multiplies them; harmonic mean uses reciprocals for rates. This hub links to each calculator, explains which one fits your data, and shows Excel equivalents for each formula.

Additive averageArithmetic Mean Calculator — Formula, Examples, and When to Use It

Arithmetic mean (AM) is the sum of all values divided by the count: AM = (x₁ + x₂ + ⋯ + xₙ) / n. It is the correct average when every value contributes equally to a total — such as test scores, temperatures, and counts. This calculator computes AM alongside geometric and harmonic mean so you can confirm which average best fits your data.

Rate & reciprocal averageHarmonic Mean Calculator — Formula, Speed Examples, and Rate Averaging

Harmonic mean (HM) is n divided by the sum of reciprocals: HM = n / (1/x₁ + 1/x₂ + ⋯ + 1/xₙ). It is the correct average when each value is a rate applied over an equal distance, budget, or unit — such as speeds over equal distances or prices per equal spending. Classic example: traveling 100 km at 30 mph and 100 km at 60 mph — the true average speed is HM = 40 mph, not the arithmetic mean of 45 mph.

Spread & dispersionVariance and Standard Deviation Calculator — Population vs Sample Formula

Variance measures the average squared distance of each value from the mean. Standard deviation is its square root — bringing the result back to the original unit. Population variance divides by n; sample variance divides by n − 1 (Bessel's correction). For dataset {4, 7, 13, 16, 20}: mean = 12, population variance = 34.8, population standard deviation = 5.90. This calculator returns both population and sample versions side by side.

ComparisonGeometric Mean vs Arithmetic Mean: Which Average Is Correct?

Arithmetic mean (AM = sum/n) is correct for additive values. Geometric mean (GM = nth root of product) is correct when values multiply or compound. For scores 72, 80, 88, 96: AM = 84 (correct). For annual return factors 1.06, 0.92, 1.15: GM = 1.038 = 3.8%/yr (correct) — AM of 1.043 overstates by 0.5 pp and compounds to the wrong ending value.

ComparisonGeometric Mean vs Harmonic Mean: Factors vs Rates

Geometric mean (GM) is correct when values multiply: growth factors, fold changes, index relatives. Harmonic mean (HM) is correct when rates share an equal denominator: equal-distance speeds, equal-budget prices per unit. For 30 mph and 60 mph over equal distance: HM = 40 mph (correct travel time), GM = 42.43 mph (wrong), AM = 45 mph (wrong by 33 minutes per 200 km).

ComparisonMean, Median, Mode, and Range: When to Use Each

Mean is the arithmetic average (sum/n). Median is the middle value when sorted. Mode is the most frequent value. Range = max − min. For {30k, 34k, 35k, 38k, 200k}: mean = $67.4k (pulled up by outlier), median = $35k (representative of typical), mode = none, range = $170k. Reporting mean alone for skewed income data overstates the typical salary by 93%.

ComparisonWhich Average Should I Use? AM, GM, HM, Median, or Mode

Arithmetic mean (AM) is correct for additive values: scores 72+80+88+96 → AM = 84. Geometric mean (GM) is correct for multiplicative values: growth factors 1.06×0.65×1.10 → GM = 0.9144 = −8.56%/yr. Harmonic mean (HM) is correct for equal-denominator rates: 30 mph and 60 mph over equal distance → HM = 40 mph. Median is correct for skewed data: incomes {$30k,$34k,$35k,$38k,$200k} → median = $35k (mean = $67.4k is 93% too high). Mode is correct for categories: survey {A,B,B,C,B,A} → mode = B.

Frequently asked questions

Do weights have to add up to 100%?

No. Weights can add to 1, 100, 60, 500, or any positive total. The formula divides by the total weight, so only relative size matters. Weights 30, 25, 20, 25 and 0.30, 0.25, 0.20, 0.25 produce the same weighted mean.

Can a weight be zero?

A zero weight means the matching value has no effect on the result. This calculator asks for positive weights to avoid accidental ignored rows. If a value should not count, remove that value and its weight before calculating.

What is the difference between weighted mean and arithmetic mean?

Arithmetic mean gives every value equal weight. Weighted mean gives each value the influence you specify. For scores 88, 92, 76, 95, AM = 87.75. With weights 30%, 25%, 20%, 25%, weighted mean = 88.35 because the higher scores carry more weight.

Is weighted mean always between the smallest and largest value?

Yes, when all weights are positive. The weighted mean of positive-weighted values cannot fall below the smallest value or above the largest value because it is a normalized blend of those values.

Can I use negative weights?

Negative weights are used in some advanced models, but they are not appropriate for ordinary grades, prices, survey counts, or portfolio allocations. This calculator uses positive weights so the result remains a clear weighted average.

Why compare weighted mean with arithmetic mean?

The gap shows how much the weights changed the result. If weighted mean and AM are close, weights have little effect. If they differ a lot, large weights are attached to values far from the unweighted center.