How To Calculate A Weighted Average (With Examples)

By Chris Kolmar - Nov. 20, 2020

Many jobs across multiple fields require the calculation of weighted averages.

Weighted averages are essential in statistical analysis, finance, and classrooms, to name a few.

The normal average of a data-set becomes less useful when certain numbers are occurring more frequently than others. In these cases, calculating a weighted average gives users a more accurate look at the data.

This article will provide you a clear explanation of how to calculate the weighted average, as well as practical examples

What Is A Weighted Average?

A weighted average is the average of a data-set that takes into account the differing degrees of importance of numbers in the set.

Each number in a data-set is multiplied by a predetermined weight value during the calculation of the weighted average.

In comparison, normal average calculations treat each number in a data-set as if they were assigned equal weight.

The step after numbers are multiplied by weights is the same for both unweighted and weighted averages. Each number is summed up and then divided by the number of elements in the set.

Using a weighted average versus a normal average can convey an entirely different picture.

This is true in situations such as calculating the benefits the average unemployed person receives. Only a portion of unemployed workers can receive benefits.

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A weighted average calculation can easily take this into account by adjusting weight values to compensate.

A normal average calculation would completely miss this detail or require more data to provide the same accurate look.

When Are Weighted Averages Used?

Weighted averages are useful anytime some values are more important than others. There are many real-world situations where this is the case.

Understanding weighted averages will be a required skill if any of your planned jobs will involve the following:

  • Statistical research studies. Suppose a survey is conducted by statisticians to assess the opinions of men and women on a particular topic. However, one gender ends up participating much less in the study than the other.

    The ratio of genders in the overall population (nearly 50:50) is much different from the study’s ratio. To compensate, the survey team may weight the responses of each gender group so that they are represented proportionally.

    Similar scenarios are widespread in any research field.

  • Classrooms. The score a student achieves on an exam may be much more important than their score on a piece of homework. Thus, the student’s exam score is given a higher weighting when their course grade is calculated.

    Weighted GPAs also require similar calculations.

  • Stock portfolio. An investor buys shares in a company over a period of time. It can be challenging for them to keep track of their average cost as stock prices fluctuate in value.

    They can solve this issue by calculating a weighted average using the prices they bought shares at as different weight values.

    Weighted averages are used extensively in financial fields, especially by quantitative analysts. You’ll need to calculate weighted averages not just for stock prices but for almost every value on a balance sheet.

  • Warehouse weight measurements. Items are often kept on separate pallets inside warehouses. A weighmaster or scale operator could be tasked with collecting accurate weight measurements of these items.

    As some lots may be drastically more filled than others, simply averaging each type of item’s weight would not suffice.

    To account for these differences, a weighted average calculation uses the quantities of each type of item as the weight value.

  • Cost accounting. Suppose a company orders varying amounts of different goods, and their senior cost accountant seeks to calculate the average cost of goods.

    Rather than merely averaging the price of each type of good, the frequency at which each was purchased must be considered.

    A weighted average calculation could consider these various frequencies as the weight value, providing a more accurate average cost calculation.

Weighted average calculations are used in many other jobs, such as by funding specialists and actuaries.

Examples of Weighted Average Calculations

Here, we’ll give you examples of weighted average calculations with real numbers to provide insight into the exact process.

A few examples will use real-world examples mentioned earlier to provide context.

Example Weighted Average Calculation in Statistical Research Studies

A research study is conducted to assess whether men and women reply “YES” to a certain question.

Suppose 30 men end up participating, while the number of women is 70.
15 men and 50 women respond “YES” to the question.

A typical mean calculation would show that (15+50)/100 = 65% of men and women would reply “YES” to the question.

However, the ratio of men to women in the general population is almost exactly 50:50.

This means women are overrepresented in the study by a factor of 70/50 = 1.4.
Men are underrepresented in the study by a factor of 50/30 = 1.667.

Therefore, the normal mean is not representative of the overall population. We require a calculation that takes into account the disproportionality of the surveyed groups.

This is precisely what weighted-averages are used for.

We want to weight the responses by men to be higher and the responses by women to be lower.

Divide the 50 women who responded “YES” by a weight of 1.4 (their overrepresentation factor).

50/1.4 = 35.71

Multiply the 15 men who responded “YES” by a weight of 1.667 (their underrepresentation factor).

15 x 1.667 = 25

The final step is to add these two values together and divide it by the number of research participants, giving us the weighted average.

(35.71 + 25)/100 = 60.71%

This weighted average percentage of 60.71% is much more representative of the population than our normal average of 65%.

Example Weighted Average Calculation in Natural Gas Trading

Natural gas traders are often interested in the volume-adjusted average price of gas in a particular region.

There are usually many gas stations within a region. Each of these varies in both price and volume of supply. A normal average calculation would not be useful, as it would not account for these different volumes.

A weighted average calculation resolves this complication. Consider the following formula:

Region price = ((Station1 price x Station1 volume) + (Station2 price x Station2 volume) + (Station3 price x Station3 volume) + …) / (Total Volume)

The above is a weighted average formula that uses each station’s volume of gas supply as the weight value. Thus, the natural gas trader can obtain the true volume-adjusted average price of gas.

Let’s now use real numbers to show the different results provided by a normal average and weighted average calculation.

The prices and volume at each station:

  • Station 1. Price = $2.15 and volume = 100 gal

  • Station 2. Price = $2.05 and volume = 150 gal

  • Station 3. Price = $1.95 and volume = 50 gal

A normal average would simply average the prices of the three stations.

Average = (2.15 + 2.05 + 1.95)/3 = 2.05

The weighted average uses the volume supplied at each station as the weight value.

Weighted average = ((2.15 x 100) + (2.05 x 150) + (1.95 x 50))/300 = 2.067

This value is the true average price of gas in the region. This difference could be critical in the success or failure of the trader.

Example Weighted Average Calculation in Classrooms

Professors and teachers need to understand weighted averages in order to calculate their students’ final grades accurately.

Exam, homework, and quiz grades are seldom equally important. Thus, weight values must be considered to obtain an authentic look at a student’s performance.

Suppose student grades are composed as follows:

  • Exams = 70%

  • Quizzes = 20%

  • Assignments = 10%

The values of each of the above categories can be used as the weight values.

Here are the scores two students have received in each of the categories:

  • Timmy. Exams = 50%, quizzes = 40%, and assignments = 70%

  • Bob. Exams = 76%, quizzes = 65%, and assignments = 12%

Now, let’s calculate their weighted grades.

Timmy’s weighted grade = (0.7 x 0.5) + (0.2 x 0.4) + (0.1 x 0.7) = 0.5 = 50%
Bob’s weighted grade = (0.7 x 0.76) + (0.2 x 0.65) + (0.1 x 0.12) = 0.674 = 67.4%

Clearly, both students should be studying harder.

Example Weighted Average Calculation in Daily Life

Calculating weighted averages isn’t just important in many math and finance-related fields, but can help you in your daily life.

Suppose John is considering the purchase of a new phone. He decides on the following system to rate how important certain features are to him:

  • Battery life = 40%

  • Camera image quality = 20%

  • Storage space = 40%

These ratings could then be used as weights to calculate the weighted average score of different phone models.

Comparing these relative scores allows John to compare phones and decide his purchase easily.

Suppose the three phones he’s considering have the following ratings:

  • New iPhone. Battery life = 5, camera image quality = 8, and storage space = 7.

  • New Android. Battery life = 4, camera image quality = 5, and storage space = 3.

  • New Huawei. Battery life = 6, camera image quality = 3, and storage space = 6.

Using each feature’s relative importance as the weight value, let’s now calculate each phone model’s weighted average score.

New iPhone score = (0.4 x 5) + (0.2 x 8) + (0.4 x 7) = 6.4
New Android score = (0.4 x 4) + (0.2 x 5) + (0.4 x 3) = 3.8
New Huawei score = (0.4 x 6) + (0.2 x 3) + (0.4 x 6) = 5.4

The iPhone has the highest score, so John now knows which phone to purchase.

Weighted Averages Are Worth Learning

Calculating a weighted average provides many benefits over a simple average.

Its use is ubiquitous, both in daily life and in numerous professional fields.

With the job market as competitive as it is, every working professional needs to grow their toolbox of skills.

Chris Kolmar

Author

Chris Kolmar

Chris Kolmar is a co-founder of Zippia and the editor-in-chief of the Zippia career advice blog. He has hired over 50 people in his career, been hired five times, and wants to help you land your next job. His research has been featured on the New York Times, Thrillist, VOX, The Atlantic, and a host of local news. More recently, he's been quoted on USA Today, BusinessInsider, and CNBC.

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