How To Calculate Weighted Average (With Examples)

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

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.

How to Calculate Weighted Average

To calculate the weighted average of a set of numbers, you multiply each value by its weight and follow up by adding the products.

Let’s go over the process step by step:

1. Identify the weights. In some scenarios, determining the weight of each value is rather straightforward, albeit arbitrary. Consider teachers who provide a syllabus clearly laying out the weight of various coursework totaling up to 100% of your final grade.

   In other cases, the weight of each value is arrived at mathematically (we’ll cover a few such examples below). In stock trading, the amount of stock you buy represents the weight. When dealing with massive sets of statistical data, the weight of a variable is determined through the use of randomized data trees to ensure an unbiased distribution.

2. Multiply the value by its weight. Once you’ve determined the weight of each value, it’s simply a matter of multiplying the weight, in decimal form, by the value. For example, if a teacher assigns tests a weight of 30%, you’d multiply your total test score by 0.3 to find your average for that category.

3. Add the results. To complete the process, add up all the weighted values. The number you wind up with is out of 100, so it can be represented as a percentage of a decimal.

How to Calculate Weighted Average Out of More or Less Than 100%

In some cases, it’s not possible to weight the values in your data set in a way that perfectly adds up to 100%. However, there is a way to determine the weighted average in such scenarios:

1. Identify the weights. Step one is essentially the same as in the above process, only your decimal places don’t add up to 1. If you don’t want to introduce bias, you can determine the frequency with which a number occurs, and then make that the variable’s weight, which will accurately show its influence over the rest of the data set.

   For example, if you tracked your daily food spending and found that:

   • 3 days you spent $15

   • 2 days you spent $35

   • 1 day you spent $20

   • 4 days you spent $10

2. Add the weights. Since your weights don’t automatically add up to 1, if you have to add them yourself. To continue the above example your sample has a total of 10 days, making that the sum of all weights.

3. Multiply each value by its weight. Now add multiply each value by its weight. So:

   • 3 x $15 = $45

   • 2 x $35 = $70

   • 1 x $20 = $20

   • 4 x $10 = $40

4. Sum each number multiplied by its weight. Add up the above numbers: 45 + 70 + 20 + 40 = 175.

5. Divide the result by the sum of weights.

   To continue our example, $175 / 10 = $17.5 is the weighted average of daily food spending.

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.

How to Calculate Weighted Average in Excel

Sometimes, weighted averages can get a bit too confusing for a pen, paper, and simple calculator. And if you’re a teacher calculating grades for dozens of students or a financial expert parsing through thousands of data points, it’s prudent to turn to Excel or similar software.

Here are a couple of ways to find the weighted average for a data set using Excel:

• Using the SUM function. If you’re familiar with the basics of Excel, you probably have some experience with the SUM function, which simply adds a set of numbers together. The trickier part is developing that set of numbers in the first place.

  To begin, place the values in one column and the weights in another column. Let’s say the values are in column C and the weights are in column D.

  Next, make a cell dedicated to your weighted average. Then, in this cell, type the formula:
  =SUM(C2*D2, C3*D3, C4*D4)

  and onwards for as many rows as you have.

  Finally, divide the result by the sum of the number of values. In Excel, this would look like
  /SUM(D2:D6)

  (with the numbers “2” and “6” representing the range of values included in the data set). In other words, you would be dividing by 5 (2, 3, 4, 5, 6).

  In total, your formula would look like this:
  =SUM(C2*D2, C3*D3, C4*D4, C5*D5, C6*D6)/SUM(D2:D6)

  This strategy is very intuitive because it’s the same as calculating weighted average by hand. Likewise, it’s only truly efficient for small data sets — otherwise, you’ll want to move onto the second option.

• Using the SUMPRODUCT function. For larger sets, it makes more sense to use the SUMPRODUCT function. Instead of multiplying each value by its weight individually, you provide a whole range of cells and tell the formula that one number is the value and the other is the weight. These ranges are called “arrays.”

  Now let’s assume the same setup as the example above, with values in column C and weights in column D. Your formula would look like
  =SUMPRODUCT(C2:C6, D2, D6)

  The formula is essentially the same as the one above, with the advantage that you don’t have to manually type in weight and value cells; simply drag your range for each array, and the formula does the rest.

  Now you simply have to divide by the sum of the total values in your set, just like in the above formula. Again, that looks like:
  /SUM(D2:D6)

  So, in total, your formula is:

  =SUMPRODUCT(C2:C6, D2, D6)/SUM(D2:D6)

Note that either approach will work with weights that don’t add up to 1 or 100%. Your results also don’t have to be expressed as percentages. These simple Excel formulas can save you a bunch of time when calculating weighted averages.

Final Thoughts

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.

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.