Weighted Mean Formula

Article byWallstreetmojo Team
Reviewed byDheeraj Vaidya, CFA, FRM

What is Weighted Mean?

The weighted mean equation is a statistical method that calculates the average by multiplying the weights with their respective mean and taking its sum. It is a type of average in which weights assign individual values to determine the relative importance of each observation.

Key Takeaways

  • The weighted mean equation is a statistical approach for calculating the average by multiplying the weights with their respective mean and taking its sum. 
  • It is a type of average where weights are assigned individual values to find each observation’s relative importance.
  • One may determine the weighted mean by multiplying the weight with the quantitative outcome and adding all the products. If all the weights are equal, then the weighted and arithmetic mean are the same.
  • The weighted mean may help an individual make decisions where some characteristics have more significance than others. 

Weighted Mean Formula

The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products. If all the weights are equal, then the weighted mean and arithmetic mean will be the same.

Weighted-Mean-Formula

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For eg:
Source: Weighted Mean Formula (wallstreetmojo.com)

Weighted Mean = ∑ni=1 (xi*wi)/∑ni=1wi

It implies that Weighted Mean = w1x1+w2x2+…+wnxn/w1+w2+…+wn

Where

  • ∑ denotes the sum
  • w is the weights and
  • x is the value

In cases where the sum of weights is 1,

Weighted Mean = ni (xi* wi)

Calculation of Weighted Mean (Step by Step)

Follow the below steps.

  1. List the numbers and weights in tabular form. Presentation in tabular form is not compulsory but makes the calculations easy.

  2. Multiply each number and the relevant weight assigned to that number (wby x1, wby x2, and so on).

  3. Add the numbers obtained in Step 2 (∑x1wi).

  4. Find the sum of the weights (∑wi).

  5. Divide the total of the values obtained in Step 3 by the sum of the weights obtained in Step 4 (∑x1wi/∑wi).

Note: If the sum of the weights is 1, then the total of the values obtained in Step 3 will be the weighted mean.

Examples

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

Example #1

The following are 5 numbers and the weights assigned to each number. Next, calculate the weighted mean of the above numbers.

Solution:

Weighted Mean Formula Example 1
Formula1
Example 1.1

WM will be –

Example 1.2

Example #2

The CEO of a company has decided that he will continue the business only if the return on capital is more than the + [Cost of Debt * % of Debt * (1-Tax Rate)]” url=”https://www.wallstreetmojo.com/weighted-average-cost-capital-wacc/”]weighted average cost of capital”Weighted”The. The company makes a return of 14% on its capital. The capital consists of equity and debt at 60% and 40%, respectively. The cost of equity is 15%, and the cost of debtCost Of DebtCost of debt is the expected rate of return for the debt holder and is usually calculated as the effective interest rate applicable to a firms liability. It is an integral part of the discounted valuation analysis which calculates the present value of a firm by discounting future cash flows by the expected rate of return to its equity and debt holders.read more is 6%. Advise the CEO on whether the company should continue with its business.

Solution:

Let us first present the given information in tabular form to understand the scenario.

We will use the following data for the calculation.

Weighted Mean Formula Example 2
Example 2.1

WM =0.60*0.15 + 0.40*0.06

= 0.090 + 0.024

Example 2.2

Since the return on capital at 14% is more than the weighted average cost of capital of 11.4%, the CEO should continue with his business.

Example #3

It is difficult to gauge the future economic scenario. The stock returns could get affected. The finance advisor develops different business scenarios and expected stock returns for each scenario. Therefore, it would enable him to make a better investment decision. Calculate the weighted mean average from the above data to help the investment advisor showcase the expected stock returns to his clients.

Solution:

We will use the following data for the calculation.

Weighted Mean Formula Example 3
Formula3
Example 3.1

=0.20*0.25 + 0.30*(-0.10) + 0.50*0.05

= 0.050 – 0.030 + 0.025

WM will be –

Example 3.2

The expected return for the stock is 4.5%.

Example #4

Jay is a rice merchant who sells various types of rice in Maharashtra. Some rice grades are of higher quality and sold at a higher price. He wants you to calculate the weighted mean from the following data:

Solution:

We will use the following data for the calculation.

Weighted Mean Formula Example 4

Step 1: In Excel, there is an inbuilt formula for calculating the products of the numbers and their sum, which is one of the steps in calculating the weighted mean. Select a blank cell and type this formula = SUMPRODUCTSUMPRODUCTThe SUMPRODUCT excel function multiplies the numbers of two or more arrays and sums up the resulting products.read more(B2: B5, C2: C5), where the range B2: B5 represents the weights and the range C2: C5 represents the numbers.

Example 4.1

Step 2:  Calculate the sum of the weights using the formula =SUM(B2: B5), where the range B2: B5 represents the weights.

Example 4.2

Step 3: Calculate =C6/B6,

Formula1
Example 4.3

WM will be –

Example 4.4

It gives the WM as Rs 51.36.

Relevance and Uses Weighted Mean Formula

Weighted mean can aid an individual in making decisions where some attributes have more significance than others. For instance, one generally uses it to calculate a specific course’s final grade. In courses, the comprehensive exam typically has more weight on the grade than chapter tests. Thus, if one performs poorly in chapter tests but does well in final exams, the weighted average of the grades will be relatively high.

One may use it in descriptive statistical analysis, such as calculating index numbers. For instance, stock market indices such as Nifty or BSE Sensex computes using the weighted average method. One can also apply it in physics to find the center of mass and moments of inertia of an object with a known density distribution.

People in business often calculate weighted mean to evaluate the average prices of goods purchased from different vendors where the quantity is considered the weight. It gives a businessman a better understanding of his expenses.

One can apply the weighted mean formula to calculate the average returns from a portfolio comprising different financial instrumentsFinancial InstrumentsFinancial instruments are certain contracts or documents that act as financial assets such as debentures and bonds, receivables, cash deposits, bank balances, swaps, cap, futures, shares, bills of exchange, forwards, FRA or forward rate agreement, etc. to one organization and as a liability to another organization and are solely taken into use for trading purposes.read more. For instance, let us assume equity consists of 80% of a portfolio and debt balance 20%. The returns from equity are 50% and from debt are 10%. The simple average would be (50%+10%)/2, which is 30%.

It gives a wrong understanding of the returns, as equity constitutes most of the portfolio. Hence, we calculate a weighted average, which works out to be 42%. This number of 42% is much closer to equity returns of 50%, as equity accounts for most of the portfolio. In other words, the returns pull by an equity weight of 80%.

Frequently Asked Questions (FAQs)

How to use the weighted mean formula?

The weighted mean is calculated by multiplying the weight or probability connected with a specific event or results with the quantitative outcome and then combining all the products.

How to get the weighted mean formula?

The formula for calculating the weighted average is the sum of all the variables multiplied by their weight. Then, one must divide it by the sum of the weights.

Can I use the weighted mean formula for non-numerical data? 

The weighted mean formula is typically used for numerical data. If you have non-numerical data, you may need to assign numerical values or scores to each category or use alternative methods for calculating the average.

Where is the weighted average used?

Weighted averages are used in statistical analysis, stock portfolios, and teacher grading averages. Moreover, it is an essential tool in accounting for stock fluctuations, uneven or misrepresented data, and assuring the same data points are equal in the represented proportion.

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