Difference Between Average and Weighted Average
The average and weighted average are both ways of computing the average; they are calculated differently. To understand the distinction between the average and weighted average, we must first understand the meaning of the two concepts. The concept of the average is taught to all of us in school. So, most of us are aware of the meaning of average. Then, what is weighted average and why is it required?
Average is a concept that is required to calculate the overall performance of a phenomenon. It is used to compute the middle value of a given set. If there are 20 boys in one class with different heights, we calculate the average height by summing their individual heights and then dividing the total by 20 to get to the average height of the class.
Thus, the average is the sum of particular observations divided by the total number of observations.
Weighted average is an average with a small difference. This concept accepts the fact that not all observations are of equal weights. If different observations are the different importance, then, each observation is multiplied by its weight and then summed up. Therefore, weighted average places importance of different observations. When we calculate the average, all observations are of similar value. On the other hand, in the weighted average, each observation has a different weightage and so the average is computed considering each observation. The concept is clear in the following example.
For example, in an examination, there is both theory and practical. However, they are not of the same importance. Therefore, to judge the performance of students in the examination, a simple average will not be enough. Here the marks obtained in theory and practical examinations are of different value. Thus, weighted average is necessary to calculate the average performance of the students.
Average is just a special case of weighted average where each value has similar or equal weightage. Similarly, weighted average is an average in which each value has a different weightage. If you need to calculate the average weight of different values, then following general formula has to be followed.
The weighted average = (a1w1 a2w2 a3w3 +anwn … ..) / (w1 w2 wn … ..)
Here ‘a’ is the value of quantities while ‘w’ is the weights of these quantities.
It is easy to compute weighted average using Microsoft excel. You need to fill in the different values of the quantities and the values of their weights in adjacent columns. With the formula tool, you can calculate the product of these two columns in a third column. Next, add the quantity values and the product column separately. Divide these two values to get the weighted average.