A weighted mean formula is usually more accurate than a simple average because, in a simple average, all the numbers in a data set are assigned an identical weight. A weighted average is an average where we assign weights to each quantity or value according to the relative importance of each value or quantity. Assume that the overall rank of a student needs to be calculated who has scored marks in different subjects and each subject has a different percentage of the total marks. For example, the written test may have 50%, the practical test may have 30% and sports may have 20% weightage in total grade marks. To calculate the weighted average, multiply each term by its weight, then divide by the sum of the weights. Remember to convert these percents to decimals before multiplying.

What is Weighted Average?

Weighted average is a statistical measure that considers the varying importance of different elements in a data set. In a standard arithmetic mean (or simple average), each data point contributes equally to the final average value. However, in a weighted average, certain data points have a greater impact on the result than others, depending on their assigned weights. The first method is used when the weights add up to one, whereas the second method is used when they do not.

What Is the Purpose of a Weighted Average?

Arithmetic means, or simple averages, are the simplest form of averaging and are widely used because of their ease of calculation and interpretation. They assume that all data points are of equal importance and are suitable for symmetrical distributions without significant outliers. Arithmetic means are easier to calculate since you simply divide the sum of the total by the number of instances. However, this method is much less nuanced and does not allow for much flexibility. Last, the interpretation of weighted averages can be more complex compared to simple arithmetic means. Though weighted averages provide a single summary statistic, they may make it tough to understand the full scope of the relationship across data points.

Why Do We Use Weighted Average Method?

This determines in advance the relative importance of each number. This is especially true when it comes to more complex sets of data. A weighted average considered all of the relative importance of each value. Once you have multiplied the weight by each value point in your data set, add all of the weighted values and divide by the total assigned weight value to arrive at the weighted average. Software like Excel and Google Sheets have made it easier to do these numbers and made them less likely to go wrong. This means that both professionals and regular people can easily use weighted averages.

• The simple average, or arithmetic mean, is when each number in a set has relative importance and is summed up and then divided by the count of numbers.
• Each of the factors is assigned some weights based on their level of importance, and then the weighted average is calculated using a mathematical formula.
• The step after numbers are multiplied by weights is the same for both unweighted and weighted averages.

Thus, the natural gas trader can obtain the true volume-adjusted average price of gas. Another common example of a weighted average is a GPA when not all classes are the same number of credits. Many colleges, for example, offer half-credit courses, one and two credit courses, three credit courses, four credit courses, and even some five credit courses.

Let’s explore the concept of weighted average by learning what it means, looking at some real-world situations, and applying the formula to solve a few examples. Calculating a weighted average provides many benefits over a simple average. A customer’s decision to buy or not to buy a product depends on the quality of the product, knowledge of the product, cost of the product, and service by the franchise. Further, the customer assigns weight to each of these criteria and calculates the weighted average.

In comparison, normal average calculations treat each number in a data set as if they were assigned equal weight. Let’s now use real numbers to show the different results provided by a normal average and weighted average calculation. The above is a weighted average formula that uses each station’s volume of gas supply as the weight value.

Whereas by using the simple average you can see that although the result is correct, it doesn’t tell the full story. Weighted averages play a pivotal role in a myriad of case studies types. In economics, they are indispensable for calculating indices like the Consumer Price Index (CPI), where goods are weighted based on consumer spending patterns. Thus, once the weight of each score is taken into account, the student’s final grade is actually lower than if each score were weighted equally. We can say that some values are more important than others, so they are multiplied by a coefficient called the weight.

But, with the help of a weighted average method, these kinds of misrepresentations can be minimised. If the weights are expressed as a percentage, then they have to add up to 100%. So as you can see, the weighted average has a lot more accuracy in what was spent and where.

When it comes to large statistical data sets such as consumer behavior data, randomized data trees can be used. This helps to ensure that the distribution of importance comes from an unbiased standpoint. This process is billing period date on subscription invoices commonly performed with the help of a computer program or software. Read on as we take a closer look in our in-depth guide on the weighted average. For each point, perform a multiplication by its corresponding weight.