The stochastic rounding (SR) function is introduced to demonstrate the effects of stochastically rounding row and column subscripts on image interpolation quality in nearest neighbor interpolation (NNI). The introduced SR function is based on a pseudorandom number that enables the pseudorandom rounding up or down of any non-integer row and column subscripts. Also, the SR function exceptionally enables rounding up of any possible cases of subscript inputs that are inferior to a pseudorandom number - especially at a high interpolation scaling ratio. The quality of NNI-SR interpolated images is evaluated against the quality of reference images - before and after applying smoothing and sharpening filters, mentioned. The quality of NNI-SR interpolated scan conversion video frames is evaluated without using any references - focusing on the quality of one frame after every 78-milliseconds for 10 000 milliseconds. Relevant experimental simulation results, discussions, and recommendations are also provided.