## Weighted Average Formula

The Weighted Average Formula is used in statistical analysis to find out the average weight of the substances that are having weights. This method helps gather more accurate information about the weights of the substances.

## What do you mean by Weighted Average?

The Weighted Average is a data set where a huge amount of data are present and only certain data are important amongst them. Weighted averages are used in stock portfolios and teacher grading averages. It is beneficial in the fields of stock fluctuations and uneven data.

## Steps to calculate the Weighted Average

**Determine the weight of each data point:**Determine the weights of the data points that prove to be useful. For example, teachers weigh tests and exams more carefully than quizzes and home works**Multiply the weight by each value:**Now, the value of each data is known, and next these data will be multiplied by each data point**Add the result of two-step together:**Now the sum of all the weighted values is calculated

## The formula for the weighted average

Let xi be the observations and wi be the weights of the observations. Then the formula for the calculation of the weighted average is given by:

W = (x_{1}w_{1} + x_{2}w_{2} + x_{3}w_{3} + x_{4}w_{4} + …) / (w_{1} + w_{2} + w_{3} + w_{4} + …)

W = sum of weighted terms / total number of terms

## Some solved examples based on the weighted average

**Q1. There are 20 students in a class. The average marks of 10 students are 70 and the rest 10 has the average marks of 80. Calculate the average score of the whole class. **

Sum of weighted terms = 10 X 70 + 10 X 80 = 700 + 800 = 1500

Now total no of terms = 20

Using the formula,

W = sum of weighted terms / total number of terms

W = 1500 / 20 = 70

The average score of the whole class is 70.

**Q2. From the table given below calculate the weighted average for the following given data: **

| 4 | 7 | 9 | 3 |

| 2 | 5 | 1 | 6 |

Sum of weighted terms = 4 X 2 + 7 X 5 + 9 X 1 + 3 X 6 = 70

Total terms = 2 + 5 + 1 + 6 = 14

W = sum of weighted terms / total number of terms

W = 70 / 14 = 5