Numerical Patterns

Weighted Average

Combine Values

A weighted average multiplies each value by its weight, sums the products, and divides by the total weight.

Program

Play the program to choose the third weight and watch the average change.

weighted_average.f90 
program weighted_average_demo
    implicit none
    real :: values(3), weights(3)
    real :: weighted_sum, weight_total, average
    real :: third_weight

    values = [10.0, 20.0, 30.0]
    third_weight = 
    weights = [1.0, 2.0, third_weight]
    weighted_sum = sum(values * weights)
    weight_total = sum(weights)
    average = weighted_sum / weight_total
    print '(F0.1)', average
end program weighted_average_demo

program weighted_average_demo
    implicit none
    real :: values(3), weights(3)
    real :: weighted_sum, weight_total, average
    real :: third_weight

    values = [10.0, 20.0, 30.0]
    third_weight = 
    weights = [1.0, 2.0, third_weight]
    weighted_sum = sum(values * weights)
    weight_total = sum(weights)
    average = weighted_sum / weight_total
    print '(F0.1)', average
end program weighted_average_demo

program weighted_average_demo
    implicit none
    real :: values(3), weights(3)
    real :: weighted_sum, weight_total, average
    real :: third_weight

    values = [10.0, 20.0, 30.0]
    third_weight = 
    weights = [1.0, 2.0, third_weight]
    weighted_sum = sum(values * weights)
    weight_total = sum(weights)
    average = weighted_sum / weight_total
    print '(F0.1)', average
end program weighted_average_demo
array product `values * weights` multiplies corresponding elements.
sum `sum(...)` reduces an array expression to one scalar.
weighted average Dividing by `sum(weights)` keeps the result on the original value scale.