How far away is pluto from earth? Does this distance vary?

It varies. The average distance is nearly the average distance of Pluto, from , 5906.4 million km = 3670.2 M miles. Interestingly this average is the same, for every other inner planet.

The distance between an inner planet and outer planet varies from (outer perihelion - inner aphelion) and (outer aphelion + inner perihelion), nearly. The average is as stated in the answer.. The error in this approximation due to the inclination 17.2 deg of Pluto's orbit to 's orbit might change the lower sd (lsd), beyond the 5th (4 here) sd. For mathematical exactitude, this inclination has to be considered for getting more than five sd.