Weighted Mean Formula

Mean is also called average in Mathematics which denotes the sum of all given quantities divided by the number of quantities. The arithmetic mean is important in statistics. For example, Let’s say there are only two quantities involved, the arithmetic mean is obtained simply by adding the quantities and dividing by 2.

If quantities are given by q₁, q₂, q₃, q₄, …… q_n

Then mean of quantities is denoted by 

= (q₁+ q₂+ q₃+ q₄+….+ q_n) / n

where n is number of quantities.

Similar to Mean, in Mathematics we also have Weighted Mean.

Weighted Mean

Weighted Mean for quantities is different from mean as, in the calculation of weighted mean, each quantity in the calculation of weighted means is assigned a weight w_x. This weight is different for different quantities and more specifically, this weight can be some kind of priority or entity associated with quantities.

Suppose the Given quantities are q₁, q₂, q₃, q₄, …… q_n

And weights associated with them are w₁, w₂, w₃, w₄, …… w_n

Then Weighted Mean is given by

Weighted Mean = (w_1×q₁ + w_2×q₂ + w_3×q₃……………….+ w_n×q_n )/ (w₁+ w₂+ w₃ +…….w_n)

Solved Questions

Question 1: Given quantities 10, 20, 30, and 40 are each associated with a weight of 2, 3, 4, and 5. Find the weighted mean of the quantities.

Answer:

Weighted Mean is given by the formula = (w_1×q₁ + w_2×q₂ + w_3×q₃……………….+ w_n×q_n )/ (w₁+ w₂+ w₃ +…….w_n)

So, Weighted Mean = (10×2+ 20×3 + 30×4 + 40×5)/ (2 + 3+ 4+ 5)

                                 = (20 + 60 + 120 + 200)/ 14

                                 = 400/ 14

                                 = 28.57

Question 2: Given quantities 50, 25, 36, and 41 are each associated with a weight of 2.5, 8, 6, and 5. Find the weighted mean of the quantities.

Answer:

Weighted Mean is given by the formula = (w_1×q₁ + w_2×q₂ + w_3×q₃……………….+ w_n×q_n)/ (w₁+ w₂+ w₃ +…….w_n)

So,  Weighted Mean  = (50×2.5 + 25×8 + 36×8 + 41×5)/ (2.5 + 8 + 6 + 5)

                                 = (125 + 200 + 288 + 205)/ 21.5

                                 = 818/ 21.5

                                 = 38.046

Question 3: Given quantities 5, 15, 20, 22, and 30 are each given a priority entity weight 1, 2, 3, 4, 5. Find the weighted mean of the quantities.

Answer:

Weighted Mean is given by the formula = (w_1×q₁ + w_2×q₂ + w_3×q₃……………….+ w_n×q_n)/ (w₁+ w₂+ w₃ +…….w_n)

So,  Weighted Mean  = (5×1 + 15×2 + 20×3 + 22×4 + 30×5)/ (1 + 2 + 3 + 4 + 5)

                                 = (5 + 30 + 60 + 88 + 150)/ 15

                                 = 333/ 15

                                 = 22.2

Question 4: Given quantities 3,4,5 is each associated with a weight 2,2,3. Find the weighted mean of the quantities.

Answer:

Weighted Mean is given by the formula = (w_1×q₁ + w_2×q₂ + w₃×q₃……………….+ w_n×q_n)/ (w₁+ w₂ + w₃ +…….w_n)

So,  Weighted Mean  = (3×2 + 4×2 + 5×3)/ (2 + 2 +3) 

                                 = (6 + 8 + 15)/ 7

                                 = 29/ 7

                                 = 4.142

Question 5: Given quantities 64, 32, 81, 49, 56, 65 is each given a priority entity weight 2, 1, 3, 4, 3, 5. Find the weighted mean of the quantities.

Answer:

Weighted Mean is given by the formula = (w_1×q₁ + w_2×q₂ + w_3×q₃……………….+ w_n×q_n)/ (w₁+ w₂+ w₃ +…….w_n)

So, Weighted Mean = (64×2 + 32×1 + 81×3 + 49×4 + 56×3 + 65×5)/ (2 + 1 + 3 + 4 + 3 + 5)

                                = (128 + 32 + 243 + 196 + 168 + 325)/ 18

                                = 1092/ 18

                                = 60.66