Calculate weighted arithmetic mean, sum of products, total weights, and percentage distribution with customizable data pairs.
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A weighted average (or weighted arithmetic mean) is an average where each data value is multiplied by a predetermined weight reflecting its relative importance, proportion, or frequency before summing and dividing by the total weight.
\bar{x}_w = \frac{\sum_{i=1}^n (w_i \cdot x_i)}{\sum_{i=1}^n w_i} = \frac{w_1 x_1 + w_2 x_2 + \dots + w_n x_n}{w_1 + w_2 + \dots + w_n}Multiply each value x_i by its weight w_i, sum all resulting products, and divide by the sum of all weights.
Scenario: Calculate final grade: Homework (85, 20% weight), Midterm (90, 30% weight), Final Exam (95, 50% weight)
Products: (85 × 20) + (90 × 30) + (95 × 50) = 1,700 + 2,700 + 4,750 = 9,150
Total weights: 20 + 30 + 50 = 100
Weighted mean: 9,150 / 100 = 91.5
No. Any non-negative numbers can serve as weights (e.g. credits, counts, probabilities). The formula divides by the total weight sum.
Use a weighted average whenever some data points contribute more significance or represent a larger portion of the total than others (such as credit hours in GPA).
A weight can be zero (which ignores the item completely), but weights in physical and statistical contexts should not be negative.
Enter each asset’s percentage return as the value and the dollar amount or portfolio percentage allocated to that asset as the weight.
Calculate the arithmetic mean, median, sum, count, variance, and standard deviation for any dataset with step-by-step steps.
Compute the arithmetic mean, median, mode, sum, count, and range for any set of numbers.
Quickly calculate percentages, find what percentage one number is of another, and compute percent changes.