Introduction to Weighted Average Calculator
Weighted average calculator is an online tool that helps you to find the average of different quantities in a couple of minutes. It evaluates the average weight from the given data set and helps to find the best quantity.
Weighted mean calculator is a valuable tool because it helps you in decision-making in which you only select that quantity which gives you better results as compared to other quantities.
What is the Weighted Average?
Weighted average is a method that is used to find the average value from the given weight data set of different types of quantities. It must be noted that here quantities do not mean the physical quantity but they mean a quantity of numbers, integers, decimals, or percentages.
It is used to make a decision when you have so many quantities and you want to find the best one of all. It is calculated with the weighted average formula.
Formula of Weighted Average
The weighted average formula is the sum of weight from the data set multiplied by total quantities and divided by its summation of weight. The average calculator with weight follows the following formula to calculate the weighted average.
$$ W \;=\; \frac{\sum_{i=1}^{n} w_i X_i}{\sum_{i=1}^{n} w_i} $$
Whereas,
- W is the total weight from the given data
- X is the total number of quantity
- n is the number of weight
How to Calculate Weighted Average by Using Weight Average Calculator
For Calculating weighted average, let's take an example of an average weighted problem to see how our weighted average calculator works. These steps are
Step 1:
Determine the given weight of each number that is given in the below example.
For example, three exam scores are
- Exam 1: 80 (weight: 0.3)
- Exam 2: 75 (weight: 0.4)
- Exam 3: 85 (weight: 0.3)
Step 2:
To find the weighted average apply the formula of average weight.
$$ Weighted\; Average \;=\; (w_1 \times x_1 + w_2 \times x_2 + ... + w_n \times x_n) / (w_1 + w_2 + ... + wn) $$
Where: w1, w2, ..., wn are the weights corresponding to values x1, x2, ..., xn respectively.
Step 3:
Now calculate the sum of each number multiplied by its weight, which multiply each weight with its cross-pounding score and then add them as shown below.
$$ \;=\; (0.3 \times 80 + 0.4 \times 75 + 0.3 \times 85) $$
$$ \;=\; (24 + 30 + 25.5) $$
$$ \;=\; 79.5 $$
Step 4:
Find the sum of weight which is equal to
$$ \;=\; (0.3 + 0.4 + 0.3) $$
$$ \;=\; 1 $$
Step 5:
After that divide the sum of each number multiplied by its weight by the sum of weight.
$$ Weighted\; Average \;=\; \frac{(0.3 \times 80 + 0.4 \times 75 + 0.3 \times 85)}{ (0.3 + 0.4 + 0.3)} $$
$$ \;=\; \frac{(24 + 30 + 25.5)}{ (0.3 + 0.4 + 0.3)} $$
$$ \;=\; \frac{79.5}{1} $$
$$ \;=\; 79.5 $$
So the weighted average score of this exam is 79.5.
Solved Example of an Average Weighted
The weighted average calculator can solve the average from the set of data but its main purpose is to let you know the step-by-step calculation process. So we are going to provide you with an answer for practicing.
Example:
Find the average weighted grades of given data
$$ Timmy\; Exams \;=\; 50%, \;quizzes \;=\; 40%, \;and\; assignments \;=\; 70% $$
$$ Bob\; Exams \;=\; 76%, \;quizzes \;=\; 65%, \;and\; assignments \;=\; 12% $$
Solution:
Change all the number values to decimal values.
$$ Timmy: 0.50,0.40, 0.70 $$
$$ Bob: 0.76, 0.65, 0.12 $$
Find the weighted mean, use the following formula,
$$ \bar{x}\;=\; \frac{(x_1 . w_1) + (x_2 . w_2) + … + (x_n . w_n)}{w_1 + w_2 + … + w_n } $$
$$ \bar{x} \;=\; \frac{(0.5 . 0.76) + (0.4 . 0.65) + (0.7 . 0.12)}{0.76 + 0.65 + 0.12} $$
$$ \bar{x} \;=\; 0.4732 $$
Then change the answer from decimal to percentage as 0.4732*100. So, the comparison between Timmy's and bob grades is 47%.
How to Use a Weighted Mean Calculator
Weighted calculator average has a simple layout that allows you to solve different types of problems immediately. You do not need to put in any external effort just follow our instructions so that you do not find any difficulty. These steps are:
- Enter the weight number value in the input field
- Enter the data value of the number in the input field
- Check your input data before clicking the calculate button to get the actual solution using the average weight method.
- Press the “Calculate” button for the solution of a weight average questions
Press the “Recalculate” button for more evaluation of the weight average example solution - You can use the load example to do more evaluation process of the average weight questions with a solution
Output of Weighted Average Calculator
Average calculator with weight gives you a solution of your input data when you click on the calculate button that starts the evaluation process. It may include as:
Result Box
You get the solution to average weight problems when you click on the result button.
Steps Box
Click on the Possible steps option to get the solution of the given average weight question from the calculator.
Benefits of Using Weighted Calculator Average
Weight average calculator is a wonderful tool for solving number problems using the average weight method. It gives you serval benefits whenever you use it to find the average from the given data set. These benefits are
- The calculator for weighted average is a reliable tool as it gives you accurate solutions to average weight problems
- Weighted averages calculator has a user-friendly tool so that anyone even a beginner can easily use it to solve the given number problems.
- You do not need to sign up before using it for the calculation of the average in the weighted mean calculator
- Weighted calculator average is a speedy tool that provides you with the solution to the given data question in a fraction of a second
- The weighted average calculator is a free online tool, so you can find it for evaluation of average weight questions without spending
- An average calculator with weight is used for practice to solve various kinds of examples of percentages, scores, and decimal data sets with the solution.
