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

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