# Mean and SD of the inverse of a population

1. Jun 23, 2013

### 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!

2. Jun 23, 2013

### 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).

3. Jun 27, 2013

### 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.

4. Jun 28, 2013

### Stephen Tashi

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") ?