Weighted Average Calculator
Calculate weighted mean from value-weight pairs. Use the Weighted Average tab — enter each value and its weight, get the weighted mean instantly alongside the unweighted mean for comparison.
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How It Works
Switch to the Weighted Average tab. Each row has a Value field and a Weight field. Add as many rows as needed. The calculator computes Σ(value×weight)/Σ(weights) and shows the weighted mean. The unweighted mean also displays for comparison — if they differ significantly, weights have a meaningful effect.
Weighted mean = Σ(xᵢ × wᵢ) / Σ(wᵢ)Physics 85(w=4), Math 90(w=3), History 78(w=2) → WA=85.11Each course: enter letter grade converted to points (A=4.0, B=3.0, C=2.0) as value, credit hours as weight. A=4.0 (3cr), B+=3.3 (4cr), C=2.0 (2cr): weighted GPA = (4.0×3 + 3.3×4 + 2.0×2)/(3+4+2) = (12+13.2+4)/9 = 29.2/9 ≈ 3.24.
GPA = Σ(grade_points × credits) / Σ(credits)A(3cr), B+(4cr), C(2cr) → GPA≈3.24Portfolio return = Σ(asset_return × weight). Weights = proportion of portfolio (must sum to 100% or 1.0). Example: 60% equities at 12% return, 30% bonds at 4%, 10% cash at 1%: weighted return = (12×0.6 + 4×0.3 + 1×0.1) = 7.2+1.2+0.1 = 8.5%. Enter returns as values and portfolio percentages as weights.
Portfolio return = Σ(rᵢ × wᵢ) weights sum to 100%60% stocks(12%) + 30% bonds(4%) + 10% cash(1%) = 8.5%Weighted average of survey responses when different respondents represent different population segments. Example: 200 urban respondents rate satisfaction 4.2, 100 rural rate it 3.1. Population-weighted average: (4.2×200 + 3.1×100)/(200+100) = (840+310)/300 = 3.83. Simple average of 4.2 and 3.1 = 3.65 — would underweight the urban majority.
Weighted mean accounts for sample size imbalancesUrban(n=200) 4.2, Rural(n=100) 3.1 → WA=3.83After computing the weighted average in the Weighted tab, switch to Descriptive Stats and enter the same values (without weights) to get mean, median, mode, SD, and quartiles. This gives context around the weighted result — if the SD is large, the weighted average may not represent any individual value well.
Weighted mean + SD + quartiles = full pictureWA=85 but SD=10 → values range widely around the meanQuick Reference
Verify these results in the calculator above.
Weighted mean
90(w=3), 80(w=1)
87.5
GPA
A=4(3cr), B=3(4cr)
3.43
Portfolio
60%(12%), 40%(4%)
8.8%
Equal weights
Equal weights 1,1,1
Same as mean
Comparison
WA vs mean for above
WA=87.5, Mean=85
Survey
Urban(n=200)4.2, Rural(n=100)3.1
3.83
Zero weight
Weight=0 effect
Value excluded
WA formula
Σ(xᵢwᵢ)/Σ(wᵢ)
Formula
Tips & Shortcuts
Weights do not need to add up to 100 or 1 — the calculator divides by the total automatically. Use raw credit hours, respondent counts, or any proportional measure as weights.
The unweighted mean also shows in the results — compare it to the weighted mean to see how much weighting changes the answer. Large difference = weights matter significantly.
For GPA, convert letter grades to grade points first (A=4.0, A−=3.7, B+=3.3, B=3.0, etc.) before entering as values.
For portfolio returns, enter weight as the percentage allocation (60, 30, 10) and value as the return percentage (12, 4, 1) — the calculator handles normalization.
If all your weights are equal, the weighted mean equals the simple mean. Use the Descriptive Stats tab instead for full statistics on equal-weight data.
Common Mistakes
Confusing weighted mean with simple mean
Simple mean divides by count; weighted mean divides by sum of weights. If a 4-credit course grade counts the same as a 1-credit course, you are using simple mean — which gives incorrect GPA.
Entering weights that represent percentages > 100 total
Weights do not need to sum to 100, but if using percentage weights make sure they represent the correct proportions. 60%+30%+10% = 100% is correct. Entering 60, 30, 10 in the weight fields works fine — the calculator normalizes automatically.
Forgetting that weight=0 excludes a value entirely
If you enter weight=0 for a value, it contributes nothing to the weighted mean. This is intentional for excluding a component, but check that zero weights are deliberate.
Mixing raw scores and percentages as values
Be consistent — either all values are on the same scale (0-100 for grades) or you are comparing incompatible quantities. Mixing a 4.0 GPA scale with a 0-100 percentage scale in the same weighted average produces a meaningless result.
Using weighted average for medians or distributions
Weighted average gives the weighted mean only — not median, mode, or any robust measure. For highly skewed weighted data, consider weighted percentiles instead, which this calculator does not compute.
How It Works
Switch to the Weighted Average tab. Each row has a Value field and a Weight field — add as many rows as needed. The calculator computes Σ(value×weight)/Σ(weights) and shows the weighted mean. The unweighted mean also displays for comparison. Weights do not need to sum to 100 — the calculator normalizes automatically.
Weighted mean = Σ(xᵢ × wᵢ) / Σ(wᵢ)Physics 85(w=4), Math 90(w=3), History 78(w=2) → WA=85.1Enter each course grade as the value and credit hours as the weight. Convert letter grades to grade points first: A=4.0, A−=3.7, B+=3.3, B=3.0, C=2.0. Example: A(3cr), B+(4cr), C(2cr). Weighted GPA = (4.0×3 + 3.3×4 + 2.0×2)/(3+4+2) = 29.2/9 ≈ 3.24. Unweighted mean of 3.1 would underrepresent the impact of the 4-credit course.
GPA = Σ(grade_points × credits) / Σ(credits)A=4.0(3cr), B+=3.3(4cr), C=2.0(2cr) → GPA≈3.24Portfolio return = Σ(asset return × portfolio weight). Enter returns as values and percentage allocations as weights. Example: 60% equities returning 12%, 30% bonds returning 4%, 10% cash returning 1%. Weighted return = (12×60 + 4×30 + 1×10)/100 = (720+120+10)/100 = 8.5%. Simple average of 12,4,1 = 5.67% — completely ignores allocation.
Portfolio return = Σ(rᵢ × wᵢ) | weights = % allocation60%(12%) + 30%(4%) + 10%(1%) = 8.5% portfolio returnWhen survey subgroups have different sample sizes but represent different population proportions, use actual population counts as weights. Example: 200 urban respondents rate satisfaction 4.2, 100 rural rate it 3.1. Unweighted mean = 3.65. Population-weighted (200+100 respondents): (4.2×200 + 3.1×100)/300 = 3.83. The weighted result better represents the overall population.
Population WA = Σ(rating × population_n) / Σ(population_n)Urban(n=200) 4.2, Rural(n=100) 3.1 → WA=3.83The calculator shows both the weighted mean and the unweighted mean from the same data. A large difference means weights matter significantly — components with high weights are pulling the average. A small difference means the weights are nearly uniform in effect. If you notice the weighted mean is much higher, a few high-weight components dominate.
WA difference = WA − simple mean90(w=3), 80(w=1): WA=87.5, simple mean=85, diff=2.5Quick Reference
Verify these in the calculator above.
Weighted mean
90(w=3), 80(w=1)
87.5
GPA
A=4.0(3cr), B=3.0(4cr)
3.43 GPA
Portfolio
60%(12%), 40%(4%)
8.8%
Equal weights
Equal weights 1,1,1
= simple mean
Formula
WA formula
Σ(x·w)/Σ(w)
Zero weight
Weight=0 effect
Value excluded
Survey
4.2(n=200), 3.1(n=100)
3.83
Comparison
WA vs mean diff
Check impact
Tips & Shortcuts
Weights do not need to add up to 100 or 1 — the calculator divides by the total automatically. Use raw credit hours, respondent counts, or any proportional measure.
The unweighted mean also shows in the results — compare it to the weighted mean to see how much weighting changes the answer.
For GPA, convert letter grades to grade points first (A=4.0, A−=3.7, B+=3.3, B=3.0, B−=2.7, C+=2.3, C=2.0) before entering as values.
For portfolio returns, enter weight as the percentage allocation (60, 30, 10) and value as the return percentage (12, 4, 1).
If all your weights are equal, the weighted mean equals the simple mean — use the Descriptive Stats tab instead for full statistics.
Frequently Asked Questions
A weighted average assigns different importance to each value. Weighted mean = Σ(value × weight) / Σ(weights). If value 90 has weight 3 and value 70 has weight 1: weighted mean = (90×3 + 70×1)/4 = 340/4 = 85. Without weights, the simple mean would be (90+70)/2 = 80.
Use the Weighted Average tab. Enter each course grade as the value and credit hours as the weight. Example: Physics 85 (4 credits), Math 90 (3 credits), History 78 (2 credits). Weighted GPA = (85×4+90×3+78×2)/(4+3+2) = 766/9 ≈ 85.1.
No. The calculator normalizes automatically: it divides by Σ(weights) regardless of their total. Weights of 1,2,3 and weights of 10,20,30 give identical results. You can use percentages (30,70), credit hours (3,4,2), or any proportional values.
Simple average gives equal importance to all values. Weighted average gives more importance to higher-weight values. They differ when weights are unequal. Example: a 4-credit course grade matters more than a 1-credit course for GPA. If all weights are equal, weighted mean = simple mean.
Portfolio return = Σ(asset return × portfolio weight). If 60% in stocks returning 10% and 40% in bonds returning 4%: weighted return = 0.6×10 + 0.4×4 = 7.6%. Each asset's contribution scales with its share of the portfolio.
A weight of 0 means that value does not contribute to the average — it is effectively excluded. The calculator handles zero weights by ignoring them in both the numerator and denominator. This is useful when a component exists but should not count in a particular scenario.
Weighted average (mean) multiplies values by weights and divides. Weighted median finds the value at which cumulative weight reaches 50%. Weighted average is sensitive to extreme values; weighted median is robust. This calculator computes weighted mean. For weighted median, use a statistics tool that supports it explicitly.
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