# Weighted Mean Formula

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## Weighted Arithmetic Mean Formula

Statistics is an excellent subject where a huge amount of data can be processed to find out an answer. It helps the analyst to make a decision based on the outcome of the calculations done. One of the methods used in calculating and analyzing data is weighted mean. The weighted mean formula is used to consider the weight of an existing datum in a set of data to get the right average or mean of the set. It is different from that of arithmetic mean. In this section, we will take a quick look at the weighted arithmetic mean formula and its applications.

### What Do You Mean By Weighted Mean?

To understand the value of weighted mean, we need to understand the meaning and formula of arithmetic mean first.

Arithmetic mean is the technical term given to how we calculate an average. In the simplest way, the sum of all the data considered is divided by the number of cases or items present in the set. If we consider an example, the arithmetic mean of 10, 20, 30, 40, and 50 is calculated in the following way.

(Total number of data)/number of cases or items = (10 + 20 + 30 + 40 + 50)/5 = 150/50 = 30

In an advanced way, the average weighted mean formula is different from that of the arithmetic mean. In this case, the occurrence of an item in a data set is considered as weight. This weight is then multiplied with its respective datum and then added. The result of the addition is then divided by the total number of items in the set or the total weight of all the items.

Let us discuss the formula and define the terms.

Suppose, the different items present in a data set are X1, X2, X3, X4, ….. Xn. These items occur in the data W1, W2, W3, W4, ……. Wn times. The weighted mean formula is represented in the following way.

Weighted mean x̅ = (W1X1 + W2X2 + W3 X3 + ……… + Wn Xn)/ (W1 + W2 + W3 + W4 + ……. + Wn)

Here, X = the items repeating in the data set

W = number of times an item is repeating in a data set

x̅ = weighted mean of the data set

### Application of Weighted Mean Formula in Research

The simplest use of the weighted mean formula in research is the calculation and findings of the most occurring item in a data set. It can be used in the sphere of research done. The test results of a class recorded over a period of time can give the average outcome using this formula.

1. Why is the Weighted Mean Formula in Research Used?

The weighted arithmetic mean formula is used as a statistical tool to find out the average or arithmetic mean in true sense using the weight or frequency of a datum or item. The number of occurrences is considered to get the right mean value.

2. How Can You Understand and Use the Average Weighted Mean Formula?

It is very simple to understand the concept behind the average weighted mean formula. Focus on the arithmetic mean formula first. Just multiply the occurrence of every item in the data set respectively to the item. Divide the result with the total number of occurrences. You will get the result of weighted mean.

3. Why Do You Need to Practice Solving Problems Related to Weighted Mean Formula

Statistics?

The prime reason for practicing solving problems in this aspect is to carefully put into values, multiply them, and perform division accurately.