Formula for calculating weighted average

To determine the average value of a set of numbers, people often use the average value, where the formula for calculating weighted average is the most common method in daily life and production. You can follow our article below to understand more about this knowledge content.

How to calculate weighted average?

What is weighted average and when to use it?

1. Definition

Weighted average, also known as weighted mean: It is the average value that reflects the importance of elements (or observation values) in that set of numbers. Each observation value is associated with a weight.

- Other concepts:

+ Numeric Rights: A quantity related to the values of a sequence of numbers, in other words, this is the component involved in the calculation process.
+ Weight: A quantity that reflects reliability or is used to compare the importance of other information / quantities for calculation purposes.

2. Usage and Applications

- Use weighted average when each element in the set of numbers plays a different important role - the value needs to be assigned a weight.
- Applications of the method of calculating weighted average:

+ Used in statistical mathematics
+ In accounting, production, business,... people often use the method of weighted average to calculate the value of exports/imports; calculate the price of goods, materials used; calculate the value of inventory,...
+ This method is also applied in calculating product wages, bonuses based on salary coefficients/days worked,...

Formula for calculating weighted average

Given:

x with a bar on top: Weighted average

x₁, x₂, ... x_n: Symbols for elements in the set of numbers

w₁, w₂, ... w_n: Corresponding weights for elements

i: The ith order of the element or weight in the range from 1 to n

Various cases of calculating weighted averages

Case 1 : Untabulated data

* For example, suppose there is a problem like this: Determine the weighted average knowing the monthly income of households (x_i) - measured in million dong and the total number of households.

* Guidance: Here's what we do:

- Calculate each value x_i.f_i and the total value

- Apply the formula for weighted average above => Careful calculation will lead to the correct answer.

Case 2 : Tabulated data

In this case, we solve the problem as follows:

- Determine the variable quantity x_i: In the tabulated series, xi is the mid-value of the intervals

+ When the series has open intervals: Take the interval width of the interval near the open interval to calculate the upper limit of the open interval => x_i = ?

+ How to calculate the upper limit of intervals with no upper limit:

* Note : Must rely on the nature of the research content to choose suitable values for x_i because this quantity depends on the way each interval is divided

- When the interval division is symmetrical, estimating x_i can be done.

- However, when the interval division is left-skewed or right-skewed => the result is meaningless. So in this case, we should use survey data and calculate by simple average to get the most accurate result.

With some of our sharing about how to calculate weighted average as above, surely will help you feel easier in calculation for study as well as in work, especially in the field of finance - accounting. Weighted average calculation is a type of math that students will learn in 7th grade, this is basic knowledge that students need to grasp.

You can also refer to our articles on the formula for simple average calculation to supplement and enhance your own mathematical knowledge.