[Maths Class Notes] on Weighted Average Formula Pdf for Exam

For a fact, “Average” and “Mean” mean the same and are used as synonyms. To calculate the average, you add all the observations followed by division by the number of observations. For example, in a family, there are 5 children weighing 20, 35, 80, 100, and 145 pounds respectively. So to find their average rate, we add all their weights (20 + 35 + 80 + 100 + 145 = 280) and then divide it with the number of children whose weights we have calculated, that is 280 / 5 = 145 pounds. The applications of average in our day to day life is huge. So, let us learn more about the average.

What is the Weighted Average? 

A weighted average is an average where we assign weights to each quantity or value according to the relative importance of each value or quantity. Let us take an example. Assume that the overall rank of a student needs to be calculated who has scored marks in different subjects and each subject has a different percentage of the total marks. For example, the written test may have 50%, the practical test may have 30% and sports may have 20% weightage in total grade marks. 

Then what is the weighted average? The weighted average of the written test will be 0.5, the practical test will be 0.3, and sports will be 0.2. The assigned weights can be zero but can never be negative. Also, if a value has the highest weight, then it will have more effect on the weighted average and vice-versa. A weighted mean formula is usually more accurate than a simple average because, in a simple average, all the numbers in a data set are assigned an identical weight.

Weighted Mean Formula

The weight that we assign to each variable varies from situation to situation, so does the formula. So, in general, we can write the weighted mean formula as:

(Ax1+Bx2+Cx3………….. Zxn)/n

The formula to calculate weighted average in excel

The weighted average can also be calculated on an excel sheet by following the given steps:

• One can use the “SUMPRODUCT” and “SUM” functions to calculate the weighted average of a given series. 

• For example, the price of 10 apples is 20 rupees and another fruit 40 rupees per 10 fruits. To measure the weighted average, use the function “=SUMPRODUCT(A2:A3, B2:B3)/SUM(B2:B3)” here A2 and A3 are the frequency of the number and the number itself whereas, B2 and B3 are the same values of another variety of fruits in this case.

Solved Examples   

1. A teacher conducted a science test of 25 students out of which 10 students scored 80 and the rest scored 60. What is the weighted average score of the entire class?

Solution: (80 marks X 10 students) + (60 marks X 15 students)

= 800+ 900

=1700

Total number of students = 25

Weighted average formula:

Weighted average formula= sum of weighted average terms/ total number of terms

=1700/25

=68

2. Class 8 has two sections A and B. There are 25 students in section A and 30 students in section B. the average marks scored by the students in section A is 75 and the average marks scored by the students of section  B is 60. Calculate the average marks obtained by the whole class.

Solution: (25 X 75) + (30 X 60)

=1875+1800

=3675

Weighted average formula:

Weighted average formula= sum of weighted average observations/ sum of weights

=3675/55

=66.81

Fun Facts About Weighted Average

1. A weighted average formula is usually more accurate than a simple average.

2. A weighted average formula is used by stock investors basically to track the cost basis of shares.

The weighted average method takes less paperwork. For example, the person who calculates the weighted average of the cost of inputs in a factory can use the same value for all the other costs. It is a simple method taking just 3 steps and compared to the other methods, this method is easy to calculate. One can fall back on this method if they want to conduct voting or any process based on proportional representation.