Simple Average Method
The simple average method is a statistical technique for calculating the mean of a set of numbers. It is also known as the arithmetic mean and is the most commonly used method for finding the central tendency of a set of data. In this method, we add up all the values in a set of data and divide the sum by the total number of values. This gives us the average value of the set of data.

For example, let's say we want to find the average score of a student in a class. We have the following scores: 80, 90, 70, 85, and 95. To find the average, we add up all the scores and divide the sum by the total number of scores:

(80 + 90 + 70 + 85 + 95) ÷ 5 = 84

Therefore, the average score of the student in the class is 84.

Weighted Average Method
The weighted average method is a statistical technique that takes into account the relative importance or weight of each value in a set of data when calculating the mean. This method is used when the values in a set of data are not equally important.

In this method, we multiply each value in the set of data by its corresponding weight, add up all the products, and divide the sum by the total weight of all the values.

For example, let's say we want to find the average score of a student in a class, but the midterm exam is worth 40% of the total grade and the final exam is worth 60%. We have the following scores:

Midterm exam score: 80, weight: 40%
Final exam score: 90, weight: 60%

To find the weighted average, we multiply each score by its corresponding weight and add up the products:

(80 × 0.40) + (90 × 0.60) = 84

Therefore, the weighted average score of the student in the class is 84.

Key Differences

- Simple average method is used when all values in a set of data are equally important, whereas weighted average method is used when the values in a set of data are not equally important.
- In simple average method, all values are given the same weight, whereas in weighted average method, each value is multiplied by its corresponding weight.
- Simple average method assigns equal importance to all values, whereas weighted average method assigns different weights to the values based on their importance.