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
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
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
This material is intended as a summary. Use your textbook for detail explanation.
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