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

[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!

 

[EnumaElish]

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

 

[shushu97]

Thanks!