Weighted Mean – Formula and Examples

Here you will learn what is weighted mean formula and how to calculate weighted mean with examples.

Let’s begin –

Weighted Mean Formula

If \(w_1\), \(w_2\), ……\(w_n\) are the weights assigned to the values \(x_1\), \(x_2\), …..\(x_n\) respectively then their weighted mean is defined as

Weighted mean = \(w_1x_1 + w_2x_2 +……+ w_nx_n\over {w_1 +…….+ w_n}\) = \({\sum_{i=1}^{n}w_ix_i}\over {\sum_{i=1}^{n}w_i}\)

Also Read : What is the Formula for Mean Median and Mode

The weights represent the relative importance of the values of the variable x. For example, prices are usually weighted by the relative quantities involved.

Example : Calculate the mean and the weighted mean for the following data of marks in a class X examination as per the weights attached to each other.

Subject	Marks	Weights
English	62	1
Mathematics	83	3
Science	79	3
Social science	74	2
Hindi	77	2

Solution :

Subject	Marks \((x_i)\)	Weights \((w_i)\)	Weights \((w_ix_i)\)
English	62	1	62
Mathematics	83	3	249
Science	79	3	237
Social science	74	2	148
Hindi	77	2	154
	\(\sum x_i\) = 375	\(\sum w_i\) = 11	\(\sum w_ix_i\) = 850

Mean = \(\sum x_i\over n\) = \(375\over 5\) = 75

Weighted Mean = \({\sum_{i=1}^{n}w_ix_i}\over {\sum_{i=1}^{n}w_i}\) = \(850\over 11\) = 77.27

Hence, Mean = 75 and the weighted mean = 77.27