# Weighted Mean Formula

## Weighted Mean Formula

An example of an average is a Weighted Mean Formula. Some data points add more “weight” than others to the final mean, as opposed to all data points contributing equally. The weighted mean is equal to the arithmetic mean (the commonly used “average”) if all of the weights are equal. In statistics, weighted means are frequently used, particularly when analysing populations.

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Students need to understand how to use the Weighted Mean Formula, so they can apply it to answer any question. They are urged to start their studies at the beginning of the semester so that they would have a solid foundation before tackling the challenging Weighted Mean Formula. Students should make an effort to comprehend the NCERT Books for their personal benefit because they form the foundation of their knowledge.

## What is Weighted Mean?

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When certain data points are weighted more heavily than others, the Weighted Mean Formula is a sort of average that assists in equitably contributing to the final mean. In statistics, it is most frequently applied when the data is related to the population. The Weighted Mean Formula is equivalent to the arithmetic mean if the weighting of the data is uniform throughout the whole collection. To better understand the idea, let’s study more about the Weighted Mean Formula, and work through a few examples.

### Weighted Mean Definition

The Weighted Mean Formula is a type of mean that is calculated by multiplying the weight connected to a specific event or outcome by its connected quantitative outcome and then adding up all the results. In other words, the Weighted Mean Formula is derived when certain values have a greater weight than others.

The sum of the product of the weights and quantities, divided by the total of the weights, is known as the weighted mean. The idea of the weighted mean is frequently applied in accounting to assign various weights based on time or priority.

### How to Calculate the Weighted Mean?

Students employ the straightforward arithmetic mean calculation to determine the average for a set of values that have been equally weighted, in which the total sum of all values is divided by the total number of items in the set. But when one number is given more weight than the others, the Weighted Mean Formula is calculated. These two easy steps can be used to compute it:

Add the weights to the set of numbers.

The provided data set, however, is more significant than the others in several values. Each of the values (x)n carries a weight (w)n. The following is the general formula to calculate the weighted mean:

Weighted mean = Σ(w)n (x̄)n/Σ(w)n

where,

x̄ = the mean value of the set of given data.

w = corresponding weight for each observation.

The formula’s straightforward stages for calculating the weight mean are as follows:

Step 1: In this step add up all the weighted values.

Step 2: Multiply the data set’s quantities and weighted values.

Step 3: Combine the values from steps 2 and 1.

Step 4: Multiply the outcome by the figure you arrived at in step 1.

### Weighted Mean Formula

In mathematics, the average value of the data is determined using the weighted mean. When calculating the weighted mean, the average value can be determined by giving various weights to some of the individual variables. When data is presented in a different fashion than the arithmetic means or sample mean, we must compute the weighted mean. The average of the data values is calculated using many sorts of means.

By giving the quantities weights, the Weighted Mean Formula makes it easier to determine the mean of the quantities. Weights are assigned to the quantities based on their level of importance. The variables x1, x2, x3, …, xn and their weights w1, w2, w3…, wn are included in the calculation for weighted mean below, accordingly. In this case, the weighted mean represents the summary value of all the accessible quantities and is comparable to the average. The units of the weighted mean are the same as those of the component values.

### Weighted Mean Vs Arithmetic Mean

Students must understand the Weighted Mean Formula before Arithmetic Mean. Here are some points mentioned below for students to understand the Weighted Mean Formula in the easiest and most understandable way.

• The sum of the quantities is divided by the weight before being multiplied by the weighted value.
• It is used in routine financial operations.
• It comes to a resolution to an issue.

Now students must know the Arithmetic Mean so that they will be able to identify the difference between Weighted Mean Formula and Arithmetic Mean.

• The sum of the quantities is divided by the total number of observations.
• It is an equation in Mathematics.
• It stands for a group of data.

Students must know the basics of Mathematics before studying complex concepts. Hence, a thorough study of Mathematics is the key to understanding.

### Weighted Mean Examples

Use example questions on the  Weighted Mean Formula if students wish to ace their tests. Students will benefit greatly from regular practice problems, which will help them fully understand the Weighted Mean Formula. When they need help, Extramarks provides examples. They will learn more about the Weighted Mean Formula as a result. Students will be able to qualify for any competitive examination if they are well-read and well-prepared for the test.