Mean and SD of the inverse of a population

[nokia8650]

If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)?

Thank you!

 

[Bacle2]

Can't you use :

E(g(X))=∫g(x)f(x)dx ,

where f(x) is the p.d.f of X?

I don't know if you know just the values E(X) and σ(X), or if you got those using the known
value f(x).

 

[haruspex]

No, it's not possible on those data alone. You might be able to derive some bounds if you know a bit more, like a minimum value for X > 0.

 

[Stephen Tashi]

If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)?

Clarify what you mean by "population". Do you mean a statistical distribution from a known family of distributions, like a "normal distribution"? Or do you mean the mean and standard deviation computed from a collection of data that comes from an unknown probability distribution ( like the "mean height of all emergency personnel in the city") ?

 

[blue_raver22]

I can say that it is possible to calculate or estimate the mean and standard deviation of the inverse population if you have the mean and standard deviation of the original population. This can be done by using the properties of inverse operations and statistical formulas.

To calculate the mean of the inverse population, you can use the formula for the weighted arithmetic mean, where the weights are the inverse values of the original population. Similarly, the standard deviation of the inverse population can be estimated using the formula for the weighted standard deviation, where again the weights are the inverse values of the original population.

However, it is important to note that the mean and standard deviation of the inverse population may not have the same interpretation or significance as the mean and standard deviation of the original population. The inverse values may have different distributions and may not follow the same patterns as the original values. Therefore, it is important to carefully consider the context and the implications of using the mean and standard deviation of the inverse population in your analysis.

In conclusion, while it is possible to calculate or estimate the mean and standard deviation of the inverse population, it is important to understand the limitations and potential differences in interpretation compared to the original population. Further research and analysis may be needed to fully understand the implications of using these values in your study.