Weighted Average

Posted in Statistics, Total Reads: 440
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Definition: Weighted Average

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.


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