Weighted Average Calculator
Simplify the process of calculating weighted averages with this convenient online tool. Input the values and respective weights for each data point, and let the calculator compute the weighted average. Whether you're dealing with grades, scores, or any other numerical data, this calculator takes into account the importance or significance of each data point based on its weight.
What is Weighted Average
Weighted average is a statistical concept that assigns different weights or importance to different data points when calculating an average. It takes into account the significance of each data point based on its weight, allowing for a more accurate representation of the overall data set.
In a simple average, also known as an arithmetic mean, all data points are given equal weightage. However, in a weighted average, certain data points are assigned higher weights than others, reflecting their relative importance or contribution to the overall average.
The weight assigned to each data point can be based on various factors, such as the frequency of occurrence, the significance of the data point, or predetermined weights assigned by the analyst or researcher.
To calculate the weighted average, you multiply each data point by its corresponding weight, sum up these products, and divide the total by the sum of the weights. The formula for weighted average is:
Weighted Average = (Data Point 1 * Weight 1 + Data Point 2 * Weight 2 + ... + Data Point n * Weight n) / (Weight 1 + Weight 2 + ... + Weight n)
Weighted averages are commonly used in various fields, including finance, economics, education, and market research. They provide a more accurate representation of the data by considering the varying importance of different data points.
Weighted average calculation
The weighted average (x) is equal to the sum of the product of the weight (wi) times the data number (xi) divided by the sum of the weights:
Weighted average Example#1
Find the weighted average of class grades (with equal weight) 70,70,80,80,80,90:
Since the weight of all grades are equal, we can calculate these grades with simple average or we can cound how many times each grade apear and use weighted average.
2×70,3×80,1×90
Weighted average Example#2
Let's say we have three different subjects with their corresponding weights and grades:
| Subject | Weight | Grade |
|---|---|---|
| Math | 40% | 90 |
| Science | 30% | 85 |
| History | 30% | 92 |
To calculate the weighted average, you need to multiply each grade by its respective weight, sum up the products, and then divide by the total weight.
In this example, the math grade is multiplied by 0.4 (40%), the science grade by 0.3 (30%), and the history grade by 0.3 (30%). The results are then summed up and divided by the total weight (1 in this case) to obtain the weighted average.
The calculations would be as follows:
Copy Code(90 * 0.4) + (85 * 0.3) + (92 * 0.3) = 36 + 25.5 + 27.6 = 89.1
Therefore, the weighted average of these grades would be 89.1.
Please note that the weights must add up to 100% (or 1 if expressed as a decimal) for accurate calculation of the weighted average.
