Weighted Average Calculation

In our day-to-day lives, we have to deal with number crunching, all the time. Be it calculating exam scores, expenses or statistics of any kind, you need to know rudimentary arithmetic concepts. Weighted average calculation is quite a simple exercise. In this Buzzle article, I provide a detailed explanation of how to calculate weighted averages as simply as possible.

What is Weighted Average?

Before I go ahead and explain how to go about calculating weighted average, let us define and understand what we mean by a weighted average. Its calculation is similar to calculating the average, but with a slight difference.

The average of a quantity is calculated after summing up all the values of that quantity and then dividing it by the total number. A weighted average is calculated by taking into consideration, additional conditions associated with each of the values for the data. That is, some values are multiplied by an extra multiplicative factor as they occur more often. Unlike an average value, in which all the values of a quantity contribute equally, in a weighted average, they contribute unequally. Some values of the particular quantity contribute more than others and that is why it is called a weighted average.

Weighted average calculation is an important tool in descriptive statistics and mathematics. If all quantities are weighted equally or contribute equally, while calculating the weighted average, it is equal to the arithmetic mean. It comes in handy when you have to combine the averages of two different sets of values and get an overall average value.

Here is the general formula for weighted average calculation:

Weighted Average = (x1 w1 + x2 w2. .+ xn wn) / (w1 + w2. . + wn) = Σi = 1 to n (xi wi) / Σi = 1 to n wi

Here 'x_i' are values of the quantity whose weighted average is being calculated, while 'w_i' are the values of the corresponding weights. So, for calculating weighted average, you must multiply values of the quantity, with their corresponding weights, add all them up and divide them by the sum of the weights. Let me explain weighted average calculation through an example in the next section.

How to Calculate Weighted Average?

To illustrate how to go about weighted average calculation, let me present an example. Consider the following numbers to be the scores of students in class A of a school: 50, 20, 30, 10, 40, 60, 40, 50,10, 30 and let the following be the scores of students in Class B: 70, 80, 20, 10, 50. The average score of 10 students in class A is 34, while the average score of 5 students in class B is 46. What is the average score of students including both classes?

This can be found out by weighted average calculation. It can be calculated by taking the weighted mean of the two average scores. The weighted average will be given by:

Weighted Average Score of Both Classes Equal To: [34 (10) + 46 (5)] / [10 + 5] = 38

So, before you make the weighted average calculation, write out the values of the quantity whose average you plan to calculate along with their corresponding weights. Then simply use the formula and substitute. Try out problems which ask for weighted average calculation with percentages, as they are quite interesting to solve.

How to Calculate Weighted Average in Excel?

Using Microsoft excel, you can easily make weighted average calculations. Just fill in the variable values and the corresponding weight values in adjacent columns. Using the formula tool, calculate the product of the first two column values in the third column. Then sum up the values in the weight column and the product column. Just set a formula to divide the sum of product values by the sum of weight values and you are done. The main thing to figure out in a weighted average calculation problem is which are the variable and which are the weights! You can use the 'SUMPRODUCT' and 'SUM' formulas available by default in Excel, to calculate the weighted average. Suppose you enter the values to be average over, in column A (From A2 to A15) and weights in column B (From B2 to B15). Then the formula for weighted average calculation in Excel would be as follows.

Weighted Average = SUMPRODUCT (A2:A15, B2:B15) / SUM (B2:B15)

Hope this article has left you in no doubt about how to go about weighted average calculation. It is a simple method in mathematics, that helps you calculate the average according to certain conditions which are expressed by the weights. Calculating weighted average is a skill that comes in handy if you invest in shares, if you are maintaining your balance sheet or even when you are solving a GRE or GMAT paper!