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` |
| Bread | 25 | 28 |
| Eggs | 30 | 35 |
| Ghee | 375 | 380 |
| Milk | 36 | 40 |
| Cheese | 440 | 500 |
| Butter | 265 | 300 |
Solution:
| Item | Price
`p_0` | Price
`p_1` | Price relative
`P=p_1/p_0 xx 100` | `log(P)` |
| Bread | 25 | 28 | `28/25 xx 100=112` | 2.0492 |
| Eggs | 30 | 35 | `35/30 xx 100=116.67` | 2.0669 |
| Ghee | 375 | 380 | `380/375 xx 100=101.33` | 2.0058 |
| Milk | 36 | 40 | `40/36 xx 100=111.11` | 2.0458 |
| Cheese | 440 | 500 | `500/440 xx 100=113.64` | 2.0555 |
| Butter | 265 | 300 | `300/265 xx 100=113.21` | 2.0539 |
| --- | --- | --- | --- | --- |
| Total | `sum p_0=1171` | `sum p_1=1283` | `sum P=667.96` | `sum log(P)=12.2771` |
1. Simple aggregative method :
`I=(sum p_1)/(sum p_0)xx100`
`=(1283)/(1171)xx100`
`=109.56`
Thus, there is a rise of `(109.56-100)=9.56%` in prices
2. Average of price relative method (using the arithmetic mean) :
`I=1/n(sum P)`
`=1/6(667.96)`
`=111.33`
Thus, there is a rise of `(111.33-100)=11.33%` in prices
3. Average of price relative method (using the geometric mean) :
`I=antilog((sum log(P))/(n))`
`=antilog(12.2771/6)`
`=antilog(2.0462)`
`=111.22`
Thus, there is a rise of `(111.22-100)=11.22%` in prices
This material is intended as a summary. Use your textbook for detail explanation.
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