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Home > Statistical Methods calculators > Weighted Index Numbers example
5. Weighted Index Numbers example ( Enter your problem )
( Enter your problem )
  1. Laspeyre's index number Example-1
  2. Paasche's index number Example-2
  3. Fisher's index number Example-3
  4. Marshall Edgeworth's index numberExample-4
  5. Dorbish-Bowley's index number Example-5
  6. Kelly's index number Example-6
  7. Walsh's index number Example-7
 		Other related methods
  1. Fixed base method and Chain base method
  2. Unweighted Index Number
  3. Fixed base method and Chain base method for bivariate grouped data
  4. Conversion of fixed base index numbers into chain base index numbers
  5. Weighted Index Numbers
  6. Weighted average method
  7. Cost of living Index number
5. Dorbish-Bowley's index number Example-5
(Previous example)		7. Walsh's index number Example-7
(Next example)

6. Kelly's index number Example-6


1. Find Kelly's index number
ItemPrice0Quantity0Price1Quantity1
Rice391401.5
Milk40124410
Bread452501.5
Banana302361.5


Solution:
Item`p_0``q_0``p_1``q_1``q_k=(q_0+q_1)/2``p_0q_k``p_1q_k`
Rice391401.51.2548.7550
Milk4012441011440484
Bread452501.51.7578.7587.5
Banana302361.51.7552.563
------------------------
Total`620``684.5`


1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(684.5)/(620) xx 100`

`=110.4`

Thus, there is a rise of `(110.4-100)=10.4%` in prices
2. Find Kelly's index number
ItemPrice0Quantity0Price1Quantity1
A10201222
B816818
C510611
D4748


Solution:
Item`p_0``q_0``p_1``q_1``q_k=(q_0+q_1)/2``p_0q_k``p_1q_k`
A1020122221210252
B81681817136136
C51061110.552.563
D47487.53030
------------------------
Total`428.5``481`


1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(481)/(428.5) xx 100`

`=112.25`

Thus, there is a rise of `(112.25-100)=12.25%` in prices
3. Find Kelly's index number
ItemPrice0Quantity0Price1Quantity1
A325528
B150360
C230130
D515612


Solution:
Item`p_0``q_0``p_1``q_1``q_k=(q_0+q_1)/2``p_0q_k``p_1q_k`
A32552826.579.5132.5
B1503605555165
C230130306030
D51561213.567.581
------------------------
Total`262``408.5`


1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(408.5)/(262) xx 100`

`=155.92`

Thus, there is a rise of `(155.92-100)=55.92%` in prices

This material is intended as a summary. Use your textbook for detail explanation.
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5. Dorbish-Bowley's index number Example-5
(Previous example)		7. Walsh's index number Example-7
(Next example)


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