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# Weighted Average Formula

• Last Updated : 01 May, 2022

Average in mathematics holds major significance. Ancient mathematics describes average as the quantity same as a single quantity describing all the available given quantities.

For given quantities X1, X2, X3, X4, …… Xn:

Average = (X1+X2+X3+X4+….+Xn) / n

An extension to average, there is another famous mathematical quantity called weighted average.

### Weighted Average

• In weighted average, each quantity is assigned a weight, which is multiplied by the quantity to calculate the average.
• The weight assigned to these quantities can be a priority number or any other entity which describes some importance to the given quantities.
• All the quantities while calculating the average were equal, but here in calculating the weighted average, the quantities are assigned different weights.

For given quantities X1, X2, X3, X4, …… Xn. Each associated with weights w1, w2, w3, w4, …… wn

Weighted Average = ( w1 × X1 + w2 × X2 + w3 × X3 + w4 × X4 +…..+ wn × Xn)/(w1 + w2 + w3 + w4 +…….+ wn)

or

W = ∑wi × xi/ ∑wi

or

W = Sum of (Product of weights with their respective quantities)/ Sum of all the weights

### Solved Questions

Question 1: The different quantities and the associated weights with them are as given below. Find their weighted average.

Sum of weights = ∑wi = 5 + 3 + 5 + 6 = 19

∑wi  xi = 4×5 + 6×3 + 2×5 + 3×6

= 20 + 18 + 10 + 18

= 66

W = ∑wi×xi/ ∑wi

= 66 /19

Question 2: The different quantities and the associated weights with them are as given below. Find their weighted average.

Sum of weights = ∑wi = 40 + 30 = 70

∑wi×xi

= 70×40 + 50×30

= 2800 + 1500

= 4300

W = ∑wi×xi/ ∑wi

= 4300/70

= 430/7

Question 3: The data values and the associated weights with them are as follows:

Sum of weights = ∑wi = 6 + 2 + 3 + 9 = 20

∑wi×xi = 80×6 + 45×2 + 60×3 + 20×9

= 480 + 90 + 180 + 180

= 930

W = ∑wi×xi/ ∑wi

W = 930/20

= 93/2

Question 4: The different quantities and the associated weights with them are as follows:

Sum of weights = ∑wi = 5 + 3 + 6 + 3 + 7 = 24

∑wi×xi = 3×5 + 6×3 + 8×6 + 4×3 + 2×7

= 15 + 18 + 48 + 12 + 14

= 107

W = ∑wi×xi/ ∑wi

= 107/24

Question 5: The quantities and the associated weights with them are as follows:

Sum of weights = ∑wi = 2 + 3 + 1 + 2 + 4 + 2 = 14

∑wi×xi = 20×2 + 30×3 + 40×1 + 50×2 + 60×4 + 70×2

= 40 + 90 + 40 + 100 + 240 + 140

= 650

W = ∑wi×xi/ ∑wi

= 650/14

= 325/7

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