Weighted average is the arithmetic mean in which each item is multiplied by its corresponding weight, based on its relative importance, and is summed and divided by the total weight.
Weighted average technique is used instead of normal arithmetic mean when
• The average to be calculated is based on different percentage values for each item
• When each item has a frequency associated with it
For example, The scores in each subject and the corresponding weightage is given. The final score can be calculated using weighted average as shown

Score 
Weightage 
Physics 
90 
25 
Chemistry 
95 
25 
Maths 
98 
50 
Weighted average of score= ((90%*25)+(95%*25)+(98%*50))/100 = 0.9525 or 95.25%
Similarly for items with frequencies, let’s take the below example
Value: 6,2,1,5,4
Occurrences: 20,40,10,15,15
Weighted average = ((6*20)+(2*40)+(1*10)+(5*15)+(4*15))/100 = 3.45
The application of weighted average in finance is in calculating stock indices using price weighted index or market capitalization weighted index.
Price weighted index:
Security 
Price 
Share 
Weighting 
A 
$3 
10 
10% 
B 
$1 
10 
3% 
C 
$7 
10 
23% 
D 
$9 
10 
30% 
E 
$10 
10 
33% 
So, in the above example stock E has the highest price and therefore has the highest weightage in the index, whereas stock B has the lowest weightage. So in such index, higher a security’s price goes, the more it will drive the index’s value.
Market Cap weighted index
Security 
Current Price 
Outstanding Shares 
Market cap 
Weighting 
A 
$3 
50 
150 
15% 
B 
$1 
50 
50 
5% 
C 
$7 
70 
490 
51% 
D 
$9 
20 
180 
19% 
E 
$10 
10 
100 
10% 


Total market cap 
970 
100% 
In the above example, even though C doesn’t have the highest price, it has the highest market cap of 51%, and hence it determines the movement of the overall index to a greater extent.