This calculator determines the weighted mean, allowing different importance levels for each value and working with any real numbers. For equal weights, use our arithmetic mean calculator; for multiplicative relationships, our geometric mean calculator; or for reciprocal relationships, our harmonic mean calculator. Compare different types of means →

Weighted Mean Calculator

Enter each value and its corresponding weight on separate lines

Weighted Mean Formula

μw = (w₁x₁ + w₂x₂ + ... + wₙxₙ) ÷ (w₁ + w₂ + ... + wₙ)
Where:
μw = weighted mean
x₁, x₂ = values
w₁, w₂ = weights

Result

Understanding Weighted Mean

The weighted mean is like a regular average, but some values count more than others. It's perfect when different items have different levels of importance.

GPA Example

Course grades and credits:

  • Math: 85% (4 credits)
  • History: 92% (3 credits)
  • Science: 78% (4 credits)

Calculation:

(85 × 4) + (92 × 3) + (78 × 4) = 884
Total credits: 4 + 3 + 4 = 11
Weighted mean = 884 ÷ 11 = 84.5%

Investment Returns

Portfolio returns and investment amounts:

  • Stock A: 12% return ($5000 invested)
  • Stock B: 8% return ($3000 invested)
  • Stock C: 15% return ($2000 invested)

Calculation:

(12 × 5000) + (8 × 3000) + (15 × 2000) = 114000
Total invested: 5000 + 3000 + 2000 = 10000
Weighted return = 114000 ÷ 10000 = 11.4%

When to Use Weighted Mean

Academic

  • • GPA calculations
  • • Course grades
  • • Project scores
  • • Research weights

Financial

  • • Portfolio returns
  • • Asset allocation
  • • Risk assessment
  • • Market indices

Research

  • • Survey analysis
  • • Population studies
  • • Quality scores
  • • Performance metrics

Common Questions

When should I use weighted mean vs. regular mean?

Use weighted mean when:

  • Some values are more important than others
  • Items have different sizes or scales
  • You need to account for varying importance levels

Use regular mean when all values have equal importance.

How do I choose weights?

Weights should reflect relative importance:

  • Course credits for GPA
  • Investment amounts for portfolio returns
  • Sample sizes for research data
  • Importance levels (1-5 scale)

Can weights be decimals?

Yes! Weights can be any positive numbers:

  • Whole numbers (1, 2, 3)
  • Decimals (0.5, 1.5)
  • Percentages (30, 70)