# Weighted Average Calculation - Now Ace in Solving It

Number crunching is inescapable. Be it calculating exam scores, expenses or statistics of any kind, you need to know rudimentary arithmetic concepts like weighted average, whose calculation is explained in here.

ScienceStruck Staff

Last Updated: Aug 4, 2018

What is Weighted Average?

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.

General formula

**Weighted Average = (x**

_{1}w_{1}+ x_{2}w_{2}. .+ x_{n}w_{n}) / (w_{1}+ w_{2}. . + 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.

Calculation Technique

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?

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

Calculation in Excel

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.

*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)**