A weighted average calculator is a tool used to calculate the average of a set of numbers, with each number being given a different weight or importance. In a weighted average, each value is multiplied by its corresponding weight, and the resulting products are then summed and divided by the sum of the weights.
The formula for calculating the weighted average is:
Weighted Average = (w1x1 + w2x2 + ... + wn*xn) / (w1 + w2 + ... + wn)
x1, x2, ..., xn are the individual values in the set
w1, w2, ..., wn are the corresponding weights for each value
To calculate the weighted average using this formula, you first multiply each value by its corresponding weight. Then, you add up all of the products and divide by the sum of the weights. This gives a result that is a weighted average of the set of values, where each value's contribution to the overall average is proportional to its weight.
What is weighted average?
Weighted average is a statistical measure that takes into account the relative importance, or weight, of each data point in a data set. It is calculated by multiplying each data point by its corresponding weight, then summing up the products and dividing by the sum of the weights.
In other words, a weighted average gives more importance to certain values in a data set than others. This is useful when some data points are more significant or representative than others, and should therefore carry more weight in the final calculation.
For example, when calculating the average grade of a student, a weighted average would be used if different assignments or exams have different point values. In this case, the grades on assignments or exams with more points would carry more weight in the final calculation of the average grade.
Weighted averages are also commonly used in finance to calculate stock market indices, where the stocks with higher market capitalization are given more weight in the calculation of the index.
How to use the weighted average calculator?
- Input your data: Enter your data set, with each value and its corresponding weight. For example, if you are calculating the weighted average of grades, you would enter each grade and its corresponding weight (e.g., 90 with a weight of 0.3, 85 with a weight of 0.2, etc.).
- Calculate the product of each value and its weight: Multiply each value by its corresponding weight.
- Add up the products: Add up all the products from step 2.
- Calculate the sum of the weights: Add up all the weights from step 1.
- Divide the sum of the products by the sum of the weights: Divide the result from step 3 by the result from step 4.
- Round the answer: Round the answer to the desired number of decimal places.
For example, let’s say you have the following grades and weights:
Grade: 90, Weight: 0.3 Grade: 85, Weight: 0.2 Grade: 95, Weight: 0.5
To find the weighted average, follow these steps:
- Input your data: 90 (weight 0.3), 85 (weight 0.2), and 95 (weight 0.5)
- Calculate the product of each value and its weight: 90 x 0.3 = 27 85 x 0.2 = 17 95 x 0.5 = 47.5
- Add up the products: 27 + 17 + 47.5 = 91.5
- Calculate the sum of the weights: 0.3 + 0.2 + 0.5 = 1
- Divide the sum of the products by the sum of the weights: 91.5 / 1 = 91.5
- Round the answer: The weighted average is 91.5.