Average or arithmetic mean can be calculated by adding all numbers and then dividing the sum by the total number of items.  This method can be applicable only when all the components are weighted equally. For example, one year the average of monthly water bill would be addition of all billed amounts for the 12 months and divide by twelve. This is because each bill cycle is almost same period of time that is for 1 month. If the constituent values are different we cannot use the average or arithmetic will not work and we have to use a weighted average. The weighted average can be defined as an average in which each value has a specific weight or value assigned to it and to calculate the average. A weighted average is mainly used when we want to calculate an average based on different percentage values or when we have values whose frequency are associated with it. Compare to average or traditional average values, weighted average is much quicker and easier. It is also useful when we deal with large data sets with hundreds or thousands of items.

Here are some of the problems based on Weighted average:

Question 1: The final grades of a competition are determined on the basis of given categories: 
Presentation - 40%, 
Confidence - 25%, 
Group performance - 25%
Individual role - 10%. 

Ramesh has earned the following scores;
Presentation - 83, 
Confidence - 75, 
Group performance - 90
Individual role - 100 

Calculate the overall grade of Ramesh. 

Solution:
In the weighted average formula each value of each category must be multiplied by its percentage followed by addition of all of these new values.

Weight average would be;
=(83 $\times$ 0.40) + (75 $\times$ 0.25) + (90 $\times$ 0.25) + (100 $\times$ 0.10) 
= 33.2 + 18.75 + 22.5 + 10 
= 84.45 or 84% 

Question 2: In a chemistry course Bhavya scored the following averages;
Tests-90
Quizzes-88
Papers-85
Homework-95

The overall grade is comprised of 30% of tests, 20% of quizzes, 20% of final exam and 20% of papers with 10% of homework.
Calculate a weighted average for overall grade.

Solution:
Weighted average would be;
(90 $\times$ 0.30) + (88 $\times$ 0 .20) + (X $\times$ 0.20) + (85 $\times$ 0.20) + (95 $\times$ 0.10)
Or, 27 + 17.6 + 0 .20X + 17 + 9.5 
Or, X = 94.5