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Weighted Average Calculator
To use weighted average calculator, enter comma-separated weight & value and click calculate button
Table of Contents:
Weighted mean calculator
Weighted average calculator is an online tool to calculate the weighted average of your grades. It lets you calculate weighted mean or grade of your semester, assignments, courses, and projects, etc. Weighted grade calculator is a smart and intuitive tool that can be used for learning purposes as well as to calculate average with the given weights.
The weighted mean calculator can be used by students, teachers, supervisors, researchers, statisticians, and mathematicians to evaluate the weighted mean. This weighted calculator provides you a simple interface to make your calculations easy.
In this content, we will discuss the weighted average definition, how to find the weighted average, the formula of weighted mean, how to calculate grades with weighted percentages, and how to use grade weight calculator.
How weighted average calculator works?
Our tool can be used as a class grade calculator because you can calculate the grades in your class by using this tool. It is an average finder that acts as a grade average calculator as well as a course grade calculator.
The grade calculator with weights simply takes the weights and grades from the user and evaluates the weighted mean in the blink of an eye. To use this calculator, follow the below steps:
- Enter the weights in the given input box by separating the values using a comma.
- Enter the values in the next input box and separate the values with commas.
- Click the Calculate button to get the average with weights.
- Use the Reset button to enter new values.
After you get your weighted average using this tool, you can improve your grades by working on the low performing courses. You can also calculate the percentage of marks for each course by using our percentage calculator.
What is the weighted average?
Weighted average or weighted arithmetic mean is a type of average that takes the significance of each value into account to calculate the average.
According to Investopedia,
“Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. In calculating a weighted average, each number in the data set is multiplied by a predetermined weight before the final calculation is made.”
A more standard definition of weighted average by Wikipedia is:
“The weighted arithmetic mean is similar to an ordinary arithmetic mean except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.”
The weighted arithmetic mean is fairly more precise than the normal mean value because of the weightage.
Weighted average formula
The weighted arithmetic mean can be calculated by using the weighted average formula. The equation of weighted mean is formed by taking the sum of the product of values and weights and dividing them by the sum of weights.
Weighted Average = (w 1 × x 1 + w 2 × x 2 + w 3 × x 3 +... + w n × x n) / (w 1 + w 2 + ... + w n)
In this equation, x represents the values and w represents the weight of each value.
The only difference between normal mean and weighted mean is that we multiply the values with weight and then add them together. Moreover, instead of dividing by the sum of the total number of values, we divide it by the sum of the weights.
How to calculate weighted average?
The weighted average can be easily calculated using our grade percentage calculator above. But, if you want to learn how to calculate weighted grades by yourself instead of using the class average calculator, you should be getting ready to dive into the calculation process.
In this section, we will explain the method to calculate weighted arithmetic mean with examples. Follow these steps to find the weighted mean of the given values.
- Determine the values and weights and write them down on paper.
- Write the weighted mean formula.
- Substitute the values in the equation.
- Solve the equation to get the weighted average.
Example – Varying weights
Lili has obtained 40 marks in chemistry, 60 in mathematics, 50 in physics, 55 in computer science, and 70 marks in history in the 2nd semester of her graduation degree. Each subject weighs 60, 70, 65, 80, and 90 respectively. Calculate the weighted average of the grades of Lili.
Solution:
Step 1: Determine the values and weights and write it down on paper.
x 1 = 40, x 2 = 60, x 3 = 50, x 4 = 55, x 5 = 70
w 1 = 60, w 2 = 70, w 3 = 65, w 4 = 80, w 5 = 90
Step 2: Write the weighted mean formula.
Weighted mean = (w 1 × x 1 + w 2 × x 2 + w 3 × x 3 +... + w n × x n) / (w 1 + w 2 + ... + w n)
Step 3: Substitute the values in the equation.
Weighted mean = (60 × 40 + 70 × 60 + 65 × 50 + 80 × 55 + 90 × 70) / (60 + 70 + 65 + 80 + 90)
Step 4: Solve the equation to get the weighted average.
Weighted average = (2400 + 4200 + 3250 + 4400 + 6300) / 365 = 20550 / 365
Weighted average = 56.30
Example – Identical weights
A dairy form produced 110, 90, 100, 120, 110, 100 liters of milk each day respectively. Calculate the weighted average of the milk produced in the dairy from in 6 days.
Note: In case of the same or identical weights, we use the occurrence of value as its weights. As you can see, 110 liters milk produced on the first and the fifth day (two times). So, its weight will be 2 and it will be included in the equation only once.
Solution:
Step 1: Determine the values and write them down on paper.
x 1 = 110, x 2 = 90, x 3 = 100, x 4 = 120, x 5 = 110, x 6 = 100
Step 2: Write the weighted mean formula.
Weighted average = (w 1 × x 1 + w 2 × x 2 + w 3 × x 3 +... + w n × x n) / (w 1 + w 2 + ... + w n)
Step 3: Substitute the values in the equation.
Weighted average = (2 × 110 + 1 × 90 + 2 × 100 + 1 × 120) / (2 + 1 + 2 + 1)
Step 4: Solve the equation to get the weighted average.
Weighted average = (220 + 90 + 200 + 120) / 6 = 630 / 6
Weighted average = 105 liters
By using these methods, you can calculate weighted arithmetic mean for any values. You can use our average grade calculator to get weighted mean at one click.
FAQs
How do you calculate a weighted average?
A weighted average is calculated by adding the product of each value and its weight and dividing it by the sum of all weights. The formula of the weighted average is:
W.A = (w 1 × x 1 + w 2 × x 2 + w 3 × x 3 +... + w n × x n) / (w 1 + w 2 + ... + w n)
How do I calculate a weighted average in Excel?
To calculate the weighted average in MS Excel, two Excel functions will be used:
- SUM
- SUMPRODUCT
First, you have to calculate the sum of the product of each value and its weight by using the SUMPRODUCT function. Then divide the result by the sum of all weights using the SUM function.
What is the formula of weighted mean?
The formula of the weighted mean is:
Weighted mean= (w 1 × x 1 + w 2 × x 2 + w 3 × x 3 +... + w n × x n) / (w 1 + w 2 + ... + w n)
Where x refers to the values and w is the weight of each value.
Why is weighted average used?
The weighted average is directly connected with the degree of importance of the values. It is used when we want more or less contribution of specific values to the final result. For example, the weight of various courses in a college is different due to the importance of the subjects.
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