Average Vs Weighted Average

Article byWallstreetmojo Team
Edited bySheeba M
Reviewed byDheeraj Vaidya, CFA, FRM

What Is Average Vs Weighted Average?

Average Weighted And Weighted Average are two different mathematical calculations or functions in Excel. An Average is a method to calculate the mean of a given data set. The common method to calculate an average is by adding the numbers, then dividing the sum with the total count of added values, i.e., if we added 5 numbers, then we divide the total/sum by 5.

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Weighted average accounts for the importance of every value in a dataset. Different values have different weights, and the calculation is made by multiplying each weight with its corresponding value. The summation of all of them is divided by the sum of the weights. However, the choice between them depends on the type of information being dealt with.

Key Takeaways

  • The Average and Weighted Average are two different mathematical calculations.
  • Average
    • It is the sum of all selected values divided by the number of values added.
    • It is used to find the median value or average value.
  • Weighted Average
    • It is a value multiplied by a weight and added up to find a solution. It is given a specific weight of value to arrive at a specific answer.
    • Its main purpose is to find the right weight or value to solve. For example, it is the average value of the principal repayment of certain bonds or loans until a principal value is paid.

Average Vs Weighted Average Explained

The Average and Weighted Average are mathematical and statistical terms in finance and business. But both are calculated differently.

A Weighted Average is calculated similarly but with a weight multiplied by each data set. For example, a company owner purchases 40,000 units of a product at $5 each and 20,000 at $7 each. We will use these units as the weight and the total number of units as the sum of all weights to calculate the Weighted Average.

So, we will get,

=$5(40,000) +$7(20,000)/40,000+20,000

= ($200,000+$140,000)/60,000

= $160,000/60,000=$5.66

So, the average weighted cost is $5.66 per unit.

With the same example, if we can calculate an average. It can be calculated by adding the values and dividing them by the count of values added. Thus we use the same example to calculate the simple average vs weighted average successfully.

What Is Average?

  • The Average is the sum of all values divided by the number of values.
  • The arithmetic formula to calculate the Average is,

“Average formula = Sum of Value / Number of Value”.

What Is Weighted Average?

  • The Weighted Average is used in the field of accounting. The main purpose is to find the right weight or value to solve.
  • It is the value of the principal repayment of certain bonds or loans until the principal value is paid.
  • It is a type of average with a small difference. All values do not carry equal weights, but different values carry different importance. Each value is multiplied by the weight and added up. It can be taken as an average in which every value has a different weight. And it is influenced by the weight of the data value.
  • The weighted value is the sum of the product of value into weight divided by the sum of weight and can be written as: –

Weighted Average  Formula  = (a1w1 + a2w2 + a3w3 + …+ anwn) / (w1 + w2 + w3 … +wn)

Examples

Let us understand the concept of simple average vs. weighted average with the help of some suitable examples from both methods.

Example #1

We will calculate the Average for the class scores of 10 students using the Average formula.

The scores of the ten students in class 50, 60, 70, 80, 65, 78, 95, 63, 58, and 91, out of 100.

  • Average formula = Sum of Value / Number of Value
  • Sum of Value = 50 + 60 + 70 + 80 + 65 + 78 + 95 + 63 + 58 + 91 = 710
  • Number of Value = 10
average

So, the average for a class of 10 students is 71.

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Example #2

We will calculate the Weighted Average of exam marks using the Weighted Average formula.

If three different exams contribute to giving final marks for a year, then there is a different weight for each exam.

For example,

  • The weight was 15% for the first exam,
  • For the second exam, the weight was 25%, and
  • For the final exam, the weight was 60%.

Now, let us assume a student scored 60 marks in the first, 70 in the second, and 80 in the final exam out of 100. Let us calculate the final marks of a student.

The formula is,

Weighted Average  Formula  = (a1w1 + a2w2 + a3w3 + …+ anwn) / (w1 + w2 + w3 … +wn)

From the above values, the formula is,

=(B4*B1)+(B5*B2)+(B6*B3)/1

=(60*15%)+(70*25%)+(80*60%)/1

=(9 + 17.5 + 48)/1

=74.5

average.1
  • So, the Weighted Average of a student is 74.5.

The above examples show us the meaning of macro average vs weighted average and how to use the formula and find the desired result. In the same way, these two concepts can be used in various scenarios to derive the required conclusion successfully. Both are widely used for statistical purposes because they are simple but easy to interpret.

Infographics

The infographics given below show the differences is a concise and systematic format. It helps the reader to interpret and remember the points easily. Here, we provide you with the top 5 differences.

Average-vs-Weighted-Average-info-updated

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Key Differences

The key difference section below highlights the critical point of differences between the two topics of macro average vs weighted average with a lot of clarity and details. Let us study them and understand the two concepts clearly. The key differences between this Average and the Weighted Average are as follows:

  • The average is the sum of all values divided by the number of values. In contrast, the Weighted Average is value multiplied by the weight, and added to find a solution.
  • An Average is a mathematical calculation, whereas the Weighted Average is used in finance.
  • The Average represents a set of data. At the same time, the Weighted Average needs to be evaluated to solve a problem.
  • One can solve the Average for the data set by using the arithmetic formula. The Weighted Average is the weight of the value to arrive at a specific answer.

Comparative Table

The comparative table below shows the differences in a tabular format points them out on the basis of their definition, formula or equation, how to calculate and the type of result obtained at the end of the calculation. Let us now look at the head-to-head differences.

BasisAverageWeighted Average
DefinitionIt is the sum of all values divided by the number of values.Value is multiplied by the weight and added up to find a solution.
EquationIt is a mathematical equation.It is applied in the daily activities of finance.
SolutionIt is a representation of a set of data.It needs to be evaluated to solve a problem.
CalculationsWe can solve it for a data set using the arithmetic formula.The component is given the weight of the value to arrive at a specific answer.

This article is a guide to what is Average Vs Weighted Average. We explain each of them with examples, infographics, the key differences & a comparative table. You may also have a look at the following articles: –

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