Weighted Mean Calculator Formula

Understand the math behind the weighted mean calculator. Each variable explained with a worked example.

Formulas Used

Weighted Mean

weighted_mean = weighted_sum / weight_total

Total Weight

total_weight = weight_total

Variables

VariableDescriptionDefault
v1Value 185
w1Weight 13
v2Value 290
w2Weight 24
v3Value 378
w3Weight 32
weighted_sumDerived value= v1 * w1 + v2 * w2 + v3 * w3calculated
weight_totalDerived value= w1 + w2 + w3calculated

How It Works

How to Compute a Weighted Mean

Formula

Weighted Mean = (v1*w1 + v2*w2 + ... + vn*wn) / (w1 + w2 + ... + wn)

Each value is multiplied by its weight before summing. The result is then divided by the sum of all weights. This is useful when some observations matter more than others, such as course grades with different credit hours.

Worked Example

A student scores 85 (3 credits), 90 (4 credits), and 78 (2 credits). What is the weighted GPA?

v1 = 85w1 = 3v2 = 90w2 = 4v3 = 78w3 = 2
  1. 01Weighted sum = 85*3 + 90*4 + 78*2 = 255 + 360 + 156 = 771
  2. 02Total weight = 3 + 4 + 2 = 9
  3. 03Weighted mean = 771 / 9 = 85.6667

Ready to run the numbers?

Open Weighted Mean Calculator