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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
4. Marshall Edgeworth's index numberExample-4
(Previous example)		6. Kelly's index number Example-6
(Next example)

5. Dorbish-Bowley's index number Example-5


1. Find Laspeyre's index number, Paasche's index number, Dorbish-Bowley's index number
ItemPrice0Quantity0Price1Quantity1
Rice391401.5
Milk40124410
Bread452501.5
Banana302361.5


Solution:
Item`p_0``q_0``p_1``q_1``p_1q_0``p_0q_0``p_1q_1``p_0q_1`
Rice391401.540396058.5
Milk40124410528480440400
Bread452501.5100907567.5
Banana302361.572605445
---------------------------
Total`740``669``629``571`


1. Laspeyre's index number

`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`

`=(740)/(669) xx 100`

`=110.61`

Thus, there is a rise of `(110.61-100)=10.61%` in prices


2. Paasche's index number

`I_P=(sum p_1q_1)/(sum p_0q_1) xx 100`

`=(629)/(571) xx 100`

`=110.16`

Thus, there is a rise of `(110.16-100)=10.16%` in prices


3. Dorbish and Bowley's price index

`I_D=(I_L + I_P)/2`

`=(110.6129+110.1576)/2`

`=(220.7705)/2`

`=110.39`

Thus, there is a rise of `(110.39-100)=10.39%` in prices
2. Find Dorbish-Bowley's index number
ItemPrice0Quantity0Price1Quantity1
A10201222
B816818
C510611
D4748


Solution:
Item`p_0``q_0``p_1``q_1``p_1q_0``p_0q_0``p_1q_1``p_0q_1`
A10201222240200264220
B816818128128144144
C51061160506655
D474828283232
---------------------------
Total`456``406``506``451`


1. Dorbish and Bowley's price index

`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`

`=((456)/(406) + (506)/(451))/2 xx 100`

`=(2.2451)/2 xx 100`

`=1.1226 xx 100`

`=112.26`

Thus, there is a rise of `(112.26-100)=12.26%` in prices
3. Find Dorbish-Bowley's index number
ItemPrice0Quantity0Price1Quantity1
A325528
B150360
C230130
D515612


Solution:
Item`p_0``q_0``p_1``q_1``p_1q_0``p_0q_0``p_1q_1``p_0q_1`
A3255281257514084
B1503601505018060
C23013030603060
D51561290757260
---------------------------
Total`395``260``422``264`


1. Dorbish and Bowley's price index

`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`

`=((395)/(260) + (422)/(264))/2 xx 100`

`=(3.1177)/2 xx 100`

`=1.5589 xx 100`

`=155.89`

Thus, there is a rise of `(155.89-100)=55.89%` in prices

This material is intended as a summary. Use your textbook for detail explanation.
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4. Marshall Edgeworth's index numberExample-4
(Previous example)		6. Kelly's index number Example-6
(Next example)


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