WEIGHTED ARITHMETIC MEAN

Sometimes the variables are associated with various weights and in those cases the A.M. can be calculated, such an arithmetic mean is known as Weighted Arithmetic Mean (W.A.M.).

For example, let us assume that the variable x₁ is associated with the weight w₁ , x₂ is associated with the weight w₂ etc. and finally, x_n is associated with the weight w_n then

Formula for Weighted Arithmetic Mean

Example 1 :

Find the weighted A.M of the price for the following data

Solution :

Here the x-values are the price of the given food stuff and the weights associated are the quantities (in Kg)

Then, the Weighted arithmetic mean

=  (w₁x₁ + w₂x₂ +.......+ w_nx_n) / (w₁ + w₂ +.......w_n)

 =  (25 ⋅ 30) + (12 ⋅ 30) + (8 ⋅ 70) / (25 + 12 + 8)

=  (750 + 360 + 560) / 45

=  1670 / 45

=  $37.11

Example 2 :

For a month, a family requires the commodities listed in the table below. The weights to each commodity is given. Find the Weighted A.M.

Solution :

Here the x-values are the price of the given food stuff and the weights associated are the quantities (in Kg)

Then, the Weighted arithmetic mean

=  (w₁x₁ + w₂x₂ +.......+ w_nx_n) / (w₁ + w₂ +.......w_n)

=  (25⋅30) + (5⋅20) + (4⋅60) + (8⋅25) + (3⋅65) / (25 + 5 + 4 + 8 + 3)

=  (750 + 100 + 240 + 200 + 195) / 45

=  1485 / 45

=  $33

Example 3 :

Find the Weighted A.M for the following data

Solution :

Here the x-values are the number of items and the weights associated are cost of item in $.

Then, the Weighted arithmetic mean

=  (w₁x₁ + w₂x₂ +.......+ w_nx_n) / (w₁ + w₂ +.......w_n)

=  (2⋅45) + (4⋅12) + (5⋅15) + (4⋅25.50) / (2 + 4 + 5 + 4)

=  (90 + 48 + 75 + 102) / 15

=  315 / 15

=  $21

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