# Weighted average

A calculation using all of the observations of a variable with each observation being assigned a weight.  The weight is the relative importance of that observation.  Each observation is multiplied by its weight.  The sum of those products is divided by the sum of the weights.  If all of the weights are equal, the result is the average most commonly used.  As an example, there are three observations of some variable – 0, 1 and 2.  If the weights applied to each of them is the same, e.g., 1, the weighted average is the sum of the three observations divided by the sum of the weights or (0+1+2)/(1+1+1) = 3/3 = 1.   If the weight given to 1 and 2 is still 1, but the weight given to 0 is increased to 4, the calculation becomes (4*0 + 1*1 + 1*2)/(4+1+1) = 3/6 = 0.5.