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

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

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