We convert polynomial function of degree nth into imprecise form to obtain an important point called conversion point. For some particular region, we collect the finite number of data points to obtain the most economical function called imprecise function. Conversion point of the functions is shown with the help of MUPAD graph. Further we study the area of the imprecise function occurred by the multiplication of sine function to know how much variation of the imprecise functions are obtained for the respective intervals. For different imprecise polynomial we study level of the rate of convergence.