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

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