Average vs Weighted Average
Average and weighted Average are both averages but are computed differently. To understand the difference between average and weighted average, we first need to understand the meaning of two terms. We all know about averages as it is taught very early in school. But what is this weighted average and what are its uses?
Average
It is a concept that is required to know the overall performance or phenomenon. If there are 10 boys in a class having different weights, we calculate their average weight by adding up their individual weights and then divide the total by 10 to arrive at the average weight of the class.
Thus average is the sum of all individual observations divided by the number of observations.
Weighted average
Basically, weighted average is also an average with a slight difference that not all observations carry equal weights. If different observations carry different importance, or weights in this case, each observation is multiplied by its weight and then added up. This is done to take into account importance of different observations as they carry significance more than others. Unlike simple average, where all the observations carry same value, in weighted average, every observation is assigned a different weightage and thus the average is calculated keeping in mind the importance of each observation. The concept will be come clear from the following example.
Say for example, theory and practical carry different weights in an exam; average weight will have to be calculated to judge the performance of the student in the subject rather than just taking simple average.
It is clear then that average is just a special case of weighted average as every value has same or equal weightage here. Conversely, weighted average can be taken as average in which every value has different weight. It is these weights that determine relative importance of each quantity on the average. So if you need to find average weight of several values, here is the general formula.
Weighted average= (a1w1+a2w2+a3w3…..+anwn)/ (w1+w2+…..wn)
Here ‘a’ is the value of the quantities while w is the weights of these quantities.
It is very easy to calculate weighted average using Microsoft excel sheet. What you need to do is to fill the values of the quantities and their weights in adjacent columns. Make use of the formula tool and calculate the product of two adjacent columns writing the product in the third column. Add up the values of quantities and also the product column. Use the formula to divide the two values obtained and you have got the weighted average.