Find index number using Simple Aggregative Method, Simple Average of Price Relative Method (using the arithmetic mean), Simple Average of Price Relative Method (using the geometric mean)

Item	Price `p_0`	Price `p_1`
Cotton	909	874
Wheat	288	305
Rice	767	910
Grams	659	573

Solution:

Item	Price `p_0`	Price `p_1`	Price relative `P=p_1/p_0 xx 100`	`log(P)`
Cotton	909	874	`874/909 xx 100=96.15`	1.9829
Wheat	288	305	`305/288 xx 100=105.9`	2.0249
Rice	767	910	`910/767 xx 100=118.64`	2.0742
Grams	659	573	`573/659 xx 100=86.95`	1.9393
---	---	---	---	---
Total	`sum p_0=2623`	`sum p_1=2662`	`sum P=407.65`	`sum log(P)=8.0214`

1. Simple aggregative method :

`I=(sum p_1)/(sum p_0)xx100`

`=(2662)/(2623)xx100`

`=101.49`

Thus, there is a rise of `(101.49-100)=1.49%` in prices

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2. Average of price relative method (using the arithmetic mean) :

`I=1/n(sum P)`

`=1/4(407.65)`

`=101.91`

Thus, there is a rise of `(101.91-100)=1.91%` in prices

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3. Average of price relative method (using the geometric mean) :

`I=antilog((sum log(P))/(n))`

`=antilog(8.0214/4)`

`=antilog(2.0053)`

`=101.24`

Thus, there is a rise of `(101.24-100)=1.24%` in prices

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