Weighted Mean Formula

What is Weighted Mean?

Weighted Mean equation is a statistical method which calculates the average by multiplying the weights with its respective mean and taking its sum. It is a type of average in which weights are assigned to individual values in order to determine the relative importance of each observation.

Weighted Mean Formula

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

Weighted-Mean-Formula

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Source: Weighted Mean Formula (wallstreetmojo.com)

Weighted Mean = ∑ni=1 (xi*wi)/∑ni=1wi

This 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. 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 weighted average cost of capital. The company makes a return of 14% on its capital. The capital consists of equity and debt in the proportion of 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 under.

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. It would enable him to make a better investment decision. Calculate the weighted mean average from the above data to help the Investment Advisor to 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 are 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 then their sum, which is one of the steps in calculating the weighted mean. Select a blank cell and type this formula = SUMPRODUCTSUMPRODUCTThe SUMPRODUCT function in excel is used to multiply the array or range and provide the sum of a product. It is to calculate a weighted average. SUMPRODUCT formula is used to calculate the sum of corresponding numbers product in one or more ranges/arrays.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, it is generally used for calculating the final grade for a specific course. In courses, typically, the comprehensive exam has more weight to the grade than chapter tests. Thus, if one performs poorly in chapter tests but does really well in final exams, the weighted average of the grades will be relatively high.

It is used in descriptive statistical analysis, such as calculating index numbers. For instance, stock market indices such as Nifty or BSE Sensex are computed using the weighted average method. It can also be applied in physics to find the center of mass and moments of inertia of an object with a known density distribution.

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

Weighted Mean formula can be applied to calculate the average returns from a portfolio comprising of different financial instruments. 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 a majority 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 the majority of the portfolio. In other words, the returns are pulled by an equity weight of 80%.

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