Weighted Mean Examples

Example 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.

Solution:

Weighted Mean is given by 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

Example 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.

Solution:

Weighted Mean is given by 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

Example 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.

Solution:

Weighted Mean is given by 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

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

Solution:

Weighted Mean is given by Formula = (w_1×q₁ + w_2×q₂ + w_3×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

Example 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.

Solution:

Weighted Mean is given by 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

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.