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The weighted average calculator is an online tool to calculate the weighted average for you at one click. It is an assistive tool that takes the simple input from the user and calculates the weighted average in no time at all. In this post, we will explain what is a weighted average, how to use our weighted average calculator, how to find weighted average and formula for weighted average.
How to use the weighted average calculator?
To use the weighted average grade calculator, follow the steps below:
- Enter the weight in the given input box separated using a comma.
- Enter the values separated by a comma in the given input box.
- Press the Calculate button to see the output.
The weighted grade calculator will calculate the weighted average for the given values using the weighted average formula. It also shows the step by step process to calculate the weighted average so that you can fully understand the concept. You can use this calculator to calculate your final grade as well. You can also use our GPA calculator to estimate your GPA on the go.
What is weighted average?
A weighted average is a calculation which takes the value of different degrees of the figures into account in a dataset. Before the final calculation is made, each number in the data set multiplies by a pre-fixed weight in the calculation of the weighted average. A weighted mean can be more accurate than the simple average where the same weight is applied to all numbers within a data set.
Weighted average formula
The weighted average formula comprises the sum of the products of weight and the values. It can be written as:
Weighted Average = (W1 * X1 + W1 * X1 + ... + WnXn) / (W1 + W2 + ... +Wn)
In this equation:
W refers to the weight, and
X refers to the value.
How to calculate a weighted average?
A weighted average can be calculated by using the above formula. We have enlisted step by step method to calculate weighted average for your grades. Apart from grades, a weighted average can also be calculated for various other purposes. Follow the steps below to calculate the weighted average:
- Write down the weights and values for each course.
- Write down the formula of weighted average.
- Substitute the values in the equation for weighted average and compute the result.
Example 1:
Let’s calculate the weighted average using an example. Suppose Jim has obtained 80, 82, 73, 81, and 78 marks in all courses he is enrolled in. The weight of each course is 50, 70, 60, 75, and 56, respectively. Calculate weighted grade average of Jim’s grades.
Solution:
Step 1: Write down the weights and values for each course.
X1 = 80, X2 = 82, X3 = 73, X4 = 81, X5 = 78
W1 = 50, W2 = 70, W3 = 60, W4 = 75, W5 = 56
Step 2: Write down the formula of weighted average.
Weighted Average = (W1 * X1 + W1 * X1 + ... + WnXn) / (W1 + W2 + ... + Wn)
Step 3: Substitute the values in the equation for weighted average and compute the result.
Weighted Average = (50 * 80 + 70 * 82 + 60 * 73 + 75 * 81 + 56 * 78) / (50 + 70 + 60 + 75 + 56)
Weighted Average = 62.34
So, the weighted average of Jim’s grades is 62.34.
Example 2:
Let’s calculate the weighted average with equal grades. Data for five days of rain in millilitre is given below. Use the weight as equal for each day rain. Calculate the average weight of rain for five consecutive days. Here is the break out of daily rain measurement.
45, 67, 85, 67, 45
Solution:
Step 1: Write down the weights and values for each course.
X1 = 45, X2 = 67, X3 = 85, X4 = 67, X5 = 45
Because the weight is equal for each value according to the problem, we will use the weight as the total number of occurrences such as 45 occurred two times, so its weight will be 2.
Step 2: Write down the formula of weighted average.
Weighted Average = (W1 * X1 + W1 * X1 + ... + WnXn) / (W1 + W2 + ... + Wn)
Step 3: Substitute the values in the equation for weighted average and compute the result.
Weighted Average = (45 * 2 + 67 * 2 + 85 * 1) / (2 + 2 + 1)
Weighted Average = 61.8
So, the weighted average for the five days raining is 61.8. You can use our weighted mean calculator above for this purpose. It a perfect tool for students, teachers, and businesses to find out the weighted average online.