Present study reports statistical media optimization for dextran production for lactic acid bacteria, isolated from Indian traditional fermented idli batter. Morphological, biochemical, and 16S rRNA sequencing analysis identified the strain as Leuconostoc mesenteroides. A sequential statistical methodology comprising of Plackett-Burman and response surface methodology (RSM) were applied to enhance the fermentative production of dextran. A quadratic polynomial equation suggested by the RSM model was then validated experientially. The predicted yield by model was 60.73 g/L. Experimental verification of the model resulted in 60.30 g/L dextran. The experimental values were found to be very close to the predicted values and hence, the model was successfully validated. Simple basal medium gave 7.83 g/L dextran. Thus dextran production was increased by 7.70 fold over the unoptimized basal medium using these statistical techniques. Structural characteristic of the dextran were determined by Fourier transform infrared, $^1H$ and $^{13}C$ nuclear magnetic resonance spectroscopic techniques.