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Question
The price of a commodity increased by 5% from 2004 to 2005, 8% from 2005 to 2006 and 77% from 2006 to 2007. Calculate the average increase from 2004 to 2007?
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Solution
In averaging ratios and percentages, the geometric mean is more appropriate.
Let us consider X represents prices at the end of the year.
| Percentage rise | X | log X |
| 5 | 105 | 2.0211 |
| 8 | 108 | 2.0334 |
| 77 | 177 | 2.2479 |
| ∑ log X = 6.3024 |
Here n = 3
GM = Antilog `((sum "log X")/"n")`
= Antilog `(6.3024)/3`
= Antilog (2.1008)
= 126.1246
Average rate of increase of price = 126.1246 – 100
= 26.1246
= 26.1%
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