Average of ln(x): Approximating with ln(average of x)

Thread starter shushu97
Start date Feb 1, 2008
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Average Function

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The discussion centers on whether the average of ln(x) can be approximated by ln(average of x) when x consists of mean and deviational components. The consensus is that this approximation is generally incorrect. The key reason is that the logarithm of a sum does not equal the sum of logarithms. Therefore, the relationship between these two expressions does not hold true. Understanding this distinction is crucial for accurate mathematical analysis.

Feb 1, 2008

shushu97

Hello

Is it correct to say that average of ln(x) can be approximated by ln(average of x) where x is composed of mean and deviational parts?

Thanks for your help!

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Feb 1, 2008

EnumaElish

Science Advisor

In general, no. That's because \log\left(\sum_i x_i\right)\ne\sum_i\log\left(x_i\right).

Last edited: Feb 1, 2008

Feb 1, 2008

shushu97

Thanks!

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