Let P be a Borel probability measure on ℝ such that where S1 and S2 are two similarity mappings on ℝ such that for all x ∈ ℝ. Such a probability measure P has support the Cantor set generated by S1 and S2. For this probability measure, in this paper, we give an induction formula to determine the optimal sets of n-means and the nth quantization errors for all n ≥ 2. We have shown that the same induction formula also works for the Cantor distribution supported by the Cantor set generated by and for all x ∈ ℝ, where ψ is the square root of the Golden ratio . In addition, we give a counter example to show that the induction formula does not work for all Cantor distributions. Using the induction formula we obtain some results and observations which are also given in this paper.