Find index number using Fixed base method by taking base year 2005, Chain base method, Fixed base method by taking average of years 2009,2010,2011

Year	Price
2005	1650
2006	1690
2007	1730
2008	1750
2009	1810
2010	1850
2011	1870
2012	1900
2013	1950

Solution:
1. Fixed base method :

`"Index Number I"=("Price of current year")/("Price of base year") xx 100`

We will find the fixed base index number by taking 2005 as base year
Base Price = 1650 for base year 2005
The index number will be taken as 100 for the price 1650 in the base year 2005

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2. Chain base method :

`"Index Number I"=("Price of current year")/("Price of preceding year") xx 100`

Price for the year 2005 is not given here.
Hence, we will take the index number for 2005 as 100.

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3. Fixed base method by taking average of years :

Average price for year `2009,2010,2011` `=(1810+1850+1870)/3=1843.3333`

`"Index Number I"=("Price of current year")/("Average base price") xx 100`

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Year	Price	Fixed base index number base year `2005` `=("Price of current year")/("Price of base year") xx 100`	Chain base index number `=("Price of current year")/("Price of preceding year") xx 100`	Index number by taking average of price in year `2009,2010,2011` `=(1810+1850+1870)/3=1843.3333` as base year price
2005	1650	`1650/1650 xx 100=100`	`1650/1650 xx 100=100`	`1650/1843.3333 xx 100=89.51`
2006	1690	`1690/1650 xx 100=102.42`	`1690/1650 xx 100=102.42`	`1690/1843.3333 xx 100=91.68`
2007	1730	`1730/1650 xx 100=104.85`	`1730/1690 xx 100=102.37`	`1730/1843.3333 xx 100=93.85`
2008	1750	`1750/1650 xx 100=106.06`	`1750/1730 xx 100=101.16`	`1750/1843.3333 xx 100=94.94`
2009	1810	`1810/1650 xx 100=109.7`	`1810/1750 xx 100=103.43`	`1810/1843.3333 xx 100=98.19`
2010	1850	`1850/1650 xx 100=112.12`	`1850/1810 xx 100=102.21`	`1850/1843.3333 xx 100=100.36`
2011	1870	`1870/1650 xx 100=113.33`	`1870/1850 xx 100=101.08`	`1870/1843.3333 xx 100=101.45`
2012	1900	`1900/1650 xx 100=115.15`	`1900/1870 xx 100=101.6`	`1900/1843.3333 xx 100=103.07`
2013	1950	`1950/1650 xx 100=118.18`	`1950/1900 xx 100=102.63`	`1950/1843.3333 xx 100=105.79`

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