Free weighted average calculator: enter values and weights to get the weighted mean, the working shown line by line, and the plain average to compare.
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Weighted average = (value 1 x weight 1 + value 2 x weight 2 + ...) / (weight 1 + weight 2 + ...).
The weights do not have to add up to 100 or to 1: dividing by their total takes care of that. Weights of 20, 30 and 50 give the same answer as 0.2, 0.3 and 0.5.
Prices: you bought 100 units at $2.50, 300 at $3.10 and 600 at $2.80. Weighted average = (2.50 x 100 + 3.10 x 300 + 2.80 x 600) / 1,000 = 2,860 / 1,000 = $2.86 per unit. The plain average of the three prices is $2.80, which ignores that most units cost $2.80 or more.
Grades: homework 90 (20%), midterm 78 (30%), final 85 (50%). Weighted average = (90 x 20 + 78 x 30 + 85 x 50) / 100 = 8,390 / 100 = 83.9. The plain average is 84.3.
Credits: a 4.0 in a 3-credit class and a 3.0 in a 4-credit class average to (4.0 x 3 + 3.0 x 4) / 7 = 24 / 7 = 3.43, not 3.5.
Multiply each value by its weight, add the results, and divide by the sum of the weights. Values 90, 78 and 85 with weights 20, 30 and 50 give 8,390 / 100 = 83.9.
No. The formula divides by the total weight, so weights of 2 and 3 work the same as 40% and 60%.
A simple average counts every value once. A weighted average counts each value in proportion to its weight, so a value with a large weight pulls the result towards it.
A value with weight zero does not count, so the calculator leaves it out. Negative weights are not used in an ordinary weighted average and are ignored.
Yes. Weighted average and weighted mean are two names for the same calculation.