Weighted Mean Calculator – Σwx ÷ Σw

A weighted mean lets some values count more than others. If homework scores 70 (weight 2) and exams score 90 (weight 3), the weighted mean is (70×2 + 90×3)/(2+3) = 410/5 = 82 — the exams pull the average above the plain 80 because they carry more mass. The calculator prints every product wᵢxᵢ, the weight total, and the contrast with the unweighted mean so the shift is visible. Grade systems are the everyday case: a syllabus weighting homework 30%, midterm 30% and final 40% computes 0.3×84 + 0.3×78 + 0.4×90 = 84.6. Portfolio returns work the same way — 60% in an 8% fund and 40% in a 4% fund yields 0.6×8 + 0.4×4 = 6.4%. The tool normalizes weights automatically (2:3 behaves like 40%:60%) and rejects negative weights.

1. 1

   Enter values and weights

   Pairs like 70 with weight 2, 90 with weight 3

2. 2

   Multiply each pair

   Every wᵢxᵢ product is listed

3. 3

   Sum products and weights

   Σwx and Σw are displayed separately

4. 4

   Divide

   x̄w = Σwx/Σw, with the unweighted mean for comparison

• 1

  Weights need only relative size — 2:3 matches 40%:60%

• 2

  The weighted mean always lies between min and max values

• 3

  Equal weights collapse to the ordinary arithmetic mean

• Dividing by the number of entries instead of Σw

• Using weights as percentages that do not sum to 1 without normalizing

• Weighting points instead of point-hours in GPA calculations

• Averaging category averages that have different weight totals