What Is An Average?
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
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
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
A weighted average formula is usually more accurate than a simple average.
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.
FAQs on Weighted Average Formula
1. What are the advantages of weighted average?
In stock and accounting, the weighted average smoothes out the fluctuations in the market. Often in survey works such as census data, a segment of a population is either over-represented or under-represented. In such a situation, the weighted average takes the uneven population into consideration and turns them into a more balanced and equal representation of the data. This is basically done when the data deals with demographics and population size. Another advantage of the weighted average is that it considers equal values to be equivalent in proportion.
2. What are the differences between average and weighted average?
Average is a mean where observations are summed up and are divided by the total number of observations. A weighted average is where we give the weight to every observation of the data before we sum it up. In simple average, every observation must be equally weighted. In weighted average, every observation has its frequency. For using a simple average, there are no specific conditions but we use a weighted average when we want to calculate the average which is based on different percentage values or when observations have their frequencies.
3. How to calculate the weighted average?
Weighted average is generally used in statistics to measure the mean or average of the given numbers, but unlike the normal average, this method calculates the average by assessing the weight of every value in the series. In this method, the value of every number is assessed based on the weight it carries in the series. It means that the frequency of a number in that series decides its value. Now, let us see how to calculate the weighted average with the help of an example:
Let us say in a class of 100, 45 students got 80 marks and 55 students got 90 marks. Then the weighted average is equal to :
45*80+ 55*90 / 100
Here, we are multiplying the marks scored by the students with the number of students and adding it to the similar marks of the other students, which is multiplied by the number of students. To find the average, we are dividing it by the total number of students in the class i.e, 100.
So, 85.5 is the weighted average of the entire class.
4. What are the uses of calculating the weighted average rather than average?
When we calculate the average of a series of numbers, we get the mean value of the numbers. The weighted average of numbers is also similar to the average but we can measure it by the frequency of its occurrence. This is a better option than the average as it takes a number according to its occurrence, unlike the normal average which considers every number similarly irrespective of its frequency.
In the case of stock market accounting, this method helps a lot as it smoothes all kinds of fluctuations in the market. This method also helps in proportional representation of people according to their population weightage which in turn helps in allocating budgets accurately for different social sector schemes. In normal methods, often, some sections are either over-represented or under-represented. But, with the help of a weighted average method, these kinds of misrepresentations can be minimised.
It also helps in maintaining consistency in measuring the costs incurred by the factories while they procure raw materials. The accountant calculates one cost at the weighted average method and this can be applied to all the costs thus, avoiding a lot of paperwork. On the other hand, this method is very simple and easy compared to other methods just including 3 steps in the process.
