1464 LearnersLast updated on June 12th, 2025
Weighted Average
Average is the ratio of the sum of the value to the total number of values. Weighted average is a type of average where a particular weight is multiplied by each value in the data set. We shall learn more about weighted average in this article.
What is Weighted Average?
Weighted average is a statistical measure where the significance is given to one or more numbers. It is used when the values in a data set have differences in the degree of importance or frequency, as it is more accurate than average. A weighted average is calculated by multiplying each number in the dataset with its assigned weight, summing the results, and then dividing by the total weight.
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How to Calculate Weighted Average?
Now, let’s see how to calculate the weighted average. It is found by dividing the sum of the weighted values by the total weight. The weighted terms are the product of the value with the assigned weight. So, weighted average = sum of the weighted terms/numbers of terms.
In other words, if we consider the terms as x1, x2, x3, x4, ….., xn and the assigned weight as w1, w2, w3, w4, …., wn. Then the weighted average = x1w1 + x2w2 + x3w3 + x4w4 + …. + xnwn / w1 + w2 + w3 +w4 + … + wn. It can be simplified into,
Weighted average = Σ(wi . xi) / Σwi
Now, let's see the step-by-step process of finding the weighted average.
Step 1: Arrange the data
Step 2: Finding the weighted term, that is, the product of the value with the weight. Then, sum up the weighted values
Step 3: Find the total number of terms
Step 4: Divide the sum of weighted values by the total weight
For example, the grades of the students in the assessments and the weightage are given below, find the weighted average.
|
Assessment |
Grade |
Weight |
|
Homework |
85 |
20% (0.2) |
|
Midterm |
78 |
30% (0.3) |
|
Final exam |
92 |
50% (0.5) |
Step 1: Arrange the data for easier calculation
|
Assessment |
Grade |
Weight |
|
Homework |
85 |
20% (0.2) |
|
Midterm |
78 |
30% (0.3) |
|
Final exam |
92 |
50% (0.5) |
Step 2: Finding the weighted term, that is, the product of the value with the weight. Then, sum up the weighted values.
The weighted term of homework = 85 × 0.2 = 17
The weighted term of midterm = 78 × 0.3 = 23.4
The weighted term of final exam = 92 × 0.5 = 46
The sum of the weights values = 17 + 23.4 + 46 = 86.4
Step 3: Identify the overall weight
Here, the total weight = 0.2 + 0.3 + 0.5 = 1
Step 4: Divide the sum of the weighted values with the total number of values.
Weighted average = the sum of the weighted values / total number of values
= 86.4 / 1 = 86.4.
Weighted Average vs. Arithmetic Mean vs. Geometric Mean
There are different methods to find the average based on the purpose. For instance, we can calculate the weighted average, arithmetic mean, and geometric mean based on the objective. Now let’s discuss the difference between them:
|
Weighted Average |
Arithmetic Mean |
Geometric Mean |
|
Is the average we use to find when a value has more significance as compared to other |
The arithmetic mean is the simple average here; all the values have equal significance |
The geometric mean is used to find the average of values that represent growth rates, ratios, or percentage changes |
|
Weighted average = sum of the weighted terms/number of terms So, weighted average = Σ(wi . xi) / Σwi |
Arithmetic mean = sum of values/number of values. So, AM = x1 + x2 + …+ xn / n |
Geometric mean = nth root of the product of the values. So, geometric mean = nx1 × x2 × x3 × ....... × xn , where n is the number of terms |
|
For instance, the weighted average is used to find the grade of a student when the exam, assignments, and attendance have different weights. |
For instance, the average is used to find the overall performance of the class. |
It is used to find the compound interest, investment returns, growth rate, and so on. |
Application of Weighted Average
Now, let’s explore what are the applications of weighted averages.
- The weighted average is used to find the average when one value has more importance than the other. That is, it helps to compare the value when each has different importance.
- To handle the skewed distribution and outliers, we use weighted averages.
- The weighted average is widely used as it gives flexibility in the application in various fields.
- To track the basic cost of the investment, we use a weighted average
- To make decisions and analyze data, we use weighted averages.
Common Mistakes and Ways to Avoid Them in Weighted Average
Students frequently make errors when working on a weighted average. To master weighted average, let's learn a few common mistakes and ways to avoid them.
Mistake 1
Not dividing the sum of weighted terms with total weight.
Students find the weighted term correctly and forget to divide the term with some weight, which is an error. So, to avoid this, they should find the sum of the weight and divide the weighted term with the total weight.
Mistake 2
Confusion Between Weight and Frequency
Students can get confused between weight and frequency. To avoid this error, they should understand what is weight and frequency. Weight is the importance of each value in the data set, whereas frequency is how often the value repeats.
Mistake 3
Not Converting Weight into Decimals
Mostly, the weight is given in percentages, so it is important to convert it to decimal before calculating the weightage average. That is, if the weight of a value is 10%, they should convert it to decimal, that is 10% is 0.10.
Mistake 4
Using the Wrong Weights
Using wrong weights for values can lead to errors. To avoid this, assign the correct weight to each value.
Mistake 5
Confusing Weighted Average with Average
Students can get confused between weighted average and average. To avoid this, they should understand when both are used. The weighted average is used when the values have different weights that are significant, and the average is used when all the values have some importance.
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Solved Example on Weighted Average
Problem 1
A student scored 80 in Math (weight: 50%), 70 in Science (weight: 30%), and 90 in English (weight: 20%). What is the weighted average?
The weighted average score is 79
Explanation
Weighted average = sum of the weighted terms/number of terms
Total weight in math = 80 × 0.50 = 40
Total weight in science = 70 × 0.30 = 21
Total weight in English = 90 × 0.20 = 18
Sum of the weighted values = 40 + 21 + 18 = 79
Summing the weights, we get: 0.50 + 0.30 + 0.20 = 1
Since the total weight is 1, the final weighted average is 79.
Problem 2
An investor holds three stocks: Stock A: $10,000 (Return: 5%) Stock B: $15,000 (Return: 8%) Stock C: $25,000 (Return: 10%) Find the weighted average return.
The average return is 8.4%
Explanation
Weighted average = sum of the weighted terms/number of terms
Weightage of stock A return = 0.05 × 10000 = 500
Weightage of stock B return = 0.08 × 15000 = 1200
Weightage of stock C return = 0.10 × 25000 = 2500
Total weight = 10000 + 15000 + 25000 = 50000
So, weighted average return = 500 + 1200 + 2500 / 50000 = 4200 / 50000 = 0.084
0.084 in percentage is 8.4%
Problem 3
A product has the following customer ratings: 5-star: 40 customers 4-star: 30 customers 3-star: 20 customers 2-star: 10 customers Find the weighted average rating.
The weighted average rating is 4 star
Explanation
Weighted average = sum of the weighted terms/number of terms
Weightage of 5-star rating = 5 × 40 = 200
Weightage of 4-star rating = 4 × 30 = 120
Weightage of 3-star rating = 3 × 20 = 60
Weightage of 2-star rating = 2 × 10 = 20
Total weight = 40 + 30 + 20 +10 = 100
So, weighted average rating = 200 + 120 + 60 + 20 / 100 = 400/100 = 4
Problem 4
A car travels 100 km at 60 km/h and another 200 km at 80 km/h. What is the weighted average speed?
The average speed is 72 km/h
Explanation
Time taken to complete each segment
Time to complete 100 km = Distance / speed = 100 / 60 = 1.667 hours
Time to complete 200 km = Distance / speed = 200 / 80 = 2.5 hours
So, total time = 1.67 + 2.5 = 4.17 hours
Total distance travelled = 100 + 200 = 300 km
So, average speed = total distance / total time = 300/4.17 = 71.942 km/h
It can be rounded to 72 km/h
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FAQs on Weighted Average
1.What is the weighted average?
2.Can the weighted average be negative?
3.What is the difference between weighted average and average?
4.What are the real-life applications of weighted averages?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
