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Weighted Average Formula

Weighted Average Formula (Table of Contents)

Weighted Average Formula

The formula for calculating Weighted Average is as follows:

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Weighted-Average-Formula

Where,

  • W denotes relative weight (in %)
  • X denotes value

Examples of Weighted Average Formula

Let’s see few examples to understand Weighted Average Formula:

Example #1

Let’s assume Anand have invested the money in following proportionate: 40% in investment A, 20% in investment B, and 40% in investment C. These investments have a rate of return as follows: Investment A as 15 %, Investment B as 10%, and Investment C as 20% respectively. We need to calculate a weighted average for the rates of return Anand would receive.

Here,

  • We have Relative weights for the investments A, B & C as 40%, 20%, and 40% respectively.
  • And, Value (Rate of Return) for the investments A, B & C as 15%, 10%, and 20% respectively.

By using the Weighted Average Formula, we get-

  • Weighted Average = W1 X1 + W2 X2 + ……+ Wn Xn
  • Weighted Average = 40%*15% + 20%*10% + 40%*20%
  • Weighted Average = 16%

This shows Anand will be receiving 16% weightage average returns from the Investments A, B & C.

Example #2 

Let’s assume Anand have enrolled in a Maths course, his final grade will be determined based on the following categories: tests 30%, final exam 40%, quizzes 15%, and homework 15%.

Anand has scored following mark in each category: Tests-80, Final exam-65, quizzes-85, homework-90. Now we have to find out the overall grade of Anand.

To calculate a weighted average with percentages, each category value must first be multiplied by its percentage. Then all of these new values must be added together.

Here,

We have Relative weights for the following categories as follows:

  • Tests 30%
  • Final exam 40%
  • quizzes 15%
  • homework 15%

And, Value (Marks) for the categories as

  • Tests-80
  • Final exam-65,
  • quizzes-85
  • homework-90

By using the Weighted Average Formula, we get-

  • Weighted Average = W1 X1 + W2 X2 + ……+ WnXn
  • Weighted Average = (30%*80) + (40%*65) + (15%*85) + (15%*90)
  • Weighted Average= 76.25 or 76%

This shows the overall grade of Anand is 76%.

Example #3 

Let’s assume Jagriti have invested money in Stocks of different companies. Jagriti portfolio comprises 30% in Stock A, 15% in Stock B, 30% in Stock C and the remaining 25% in Stock D. The expected return as per the current market situation on these Stocks are as follows: Return on Stock A is 15 %, Return on Stock B is 12 %, Return on Stock C is 17% and Return on Stock D is 16 % respectively. Jagriti wants to calculate her average return on the portfolio as per the current market situation.

Here,

  • We have Relative weights of the stocks in the portfolio as follows: A, B, C & D as 30%, 15%, 30%, and 25% respectively.
  • And, Value (Rate of Return) for the stocks as follows: A, B, C & D as 15%, 12%, 17%, and 16% respectively.

By using the Weighted Average Formula, we get-

  • Weighted Average = W1 X1 + W2 X2 + W3 X3 + W4 X4 ……+ Wn Xn
  • Weighted Average = (30%*15%) + (15%*12%) + (30%*17%) + (25%*16%)
  • Weighted Average = 0.154 or 15.4%

This shows Jagriti will be receiving 15.4% weightage average returns from the Portfolio of stocks A, B, C, and D.

Explanation of Weighted Average Formula

The weighted average formula is used for calculating the average value for a particular set of numbers with different levels of relevancy. The weights must be represented in terms of total relevancy as a percentage. The weights taken should be equal to 100%, or 1.

To Calculate Weighted Average Formula, we need Relative Weightage and Value.

The first component is Relative Weightage and the second component is Value inputs. To calculate Weighted Average, we must have specific weightage for each variable taken as value and the weightage must equal to 100%.

Significance and Use of Weighted Average Formula

The weighted average is used in various financial formulas. Few examples of Weighted average beta and a weighted average cost of capital (WACC).

We are familiar with the idea of finding the athematic mean or average for a series of items. We can simply add up values of all the items and divide it by the total number of items for calculating the average. This will only work if all the items are weighted equally. For example, for calculating the average monthly mobile bills for a year, we can simply add up the total billed amounts for the past twelve months and divide it by twelve, then we can get a rough idea for the average bill paid, since the mobile bill cycle is roughly for the same period of time i.e., One month.

Now, let’s say you want to calculate the current average course grade in your Maths class. Usually, most of the classes assign different weight to exams than to homework assignments, internal test, and competitions. In this case, you need to calculate a weighted average, which takes the specific weight to each topic to calculate your course grade.

Example of a few cases where to have to use a weighted average instead of a simple average. First case- When we want to calculate an average that has different percentage values for different categories. The above example of the course grade is one the similar cases. And Secondly when we have a large group of items with a different regularity.

If a company have a wide fluctuation of sales due to the production of a seasonal product then they can use the weighted average formula. And the company wants to calculate the average for their variable expenses, then the company can use the weighted average formula and take the sales as the weight to get a better understanding of their expenses. And can compare the amount they produce or sell.

Weighted Average Calculator

You can use the following Weighted Average Calculator

W1
X1
W2
X2
W3
X3
W4
X4
Weighted Average Formula
 

Weighted Average Formula = W1*X1 + W2*X2 + W3*X3 + W4*X4
0 * 0 + 0 * 0 + 0 * 0 + 0 * 0 = 0

Weighted Average Formula in Excel (With Excel Template)

Here we will do the same example of the Weighted Average formula in Excel. It is very easy and simple. You need to provide the two inputs i.e Relative weights and Rate of Return.

You can easily calculate the Weighted Average using Formula in the template provided.

weightage average returns from the Investments A, B & C is calculated as:

(A, B & C is calculated )

overall grade of Anand is calculated as:

(overall grade of Anand )

weight Age average returns from the Portfolio of stocks A, B, C, and D is calculated as:

Portfolio of stocks

You can download this Weighted Average Formula Excel Template here – Weighted Average Formula Excel Template

Recommended Articles

This has been a guide to a Weighted Average formula. Here we discuss its uses along with practical examples. We also provide you with a Weighted Average Calculator with downloadable excel template. You may also look at the following articles to learn more –

  1. How to Calculate Overhead Ratio?
  2. Calculate Equity Multiplier With Examples
  3. Use of Gross Profit Margin Formula
  4. Guide to the Calculation of Accounts Receivables Turnover
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