Abstract: In 1885, the celebrated Weierstrass Approximation Theorem heralded intermittent interest in polynomial approximation, which continues unabated even as of today. In 1957, Baskakov proposed an infinite polynomial approximation of functions. In 1967, Lupas found it of particular use in approximating functions which are believed to be convex. In 1984, Lehnhoff proposed and studied a finite series curtailment of a similar infinite polynomial approximation by Szasz-Mirakjan operator, for good practical reasons. Motivated by the same practical reasons, we have proposed a likewise finite series curtailment of the Baskakov polynomial approximation operator. Further than that, this paper dwells upon constructing an iterative algorithm with an intention of improving the degree of approximation by this, say Modified Baskakov Operator/Polynomial Approximator. The perspective motivating the proposed algorithm is Statistical and works through a fuller use of the information, about the unknown function f being approximated, which is available in terms of its known values at equidistant knots in say [0; 1], without any loss of generality. This information is used Aposteriori to improve upon the approximation by the proposed Modified Baskakov Operator/Polynomial Approximator. This improvement turns out to be available iteratively, which is seminal to the iterative nature of the proposed algorithm of the improvement of the degree of approximation by the Modified Baskakov Operator. The potential of the aforesaid improvement algorithm is tried to be brought forth and illustrated through an Empirical Simulation Study for which the function is assumed to be known in the sense of Simulation.