Weighted Average Calculation

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.

Weighted average is an important concept in descriptive statistics and mathematics. If all quantities are weighted equally or contribute equally, while calculating the 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.

Weighted Average = (x₁ w₁ + x₂ w₂. .+ x_n w_n) / (w₁ + w₂. . + w_n) = Σ_{i = 1 to n} (x_i w_i) / Σ_{i = 1 to n} w_i

Here 'x_i' are values of the quantity whose 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.

Consider the following numbers to be the scores of students in class A: 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 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 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.

Using Microsoft excel, you can easily make these 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 such a calculation problem is which are the 'variables' 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 calculation in Excel would be as follows.

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

This is a simple method in mathematics, which helps you calculate the average according to certain conditions which are expressed by the weights. Calculating the 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.