Why do the mean, median, and mode coincide at 0 on the normal curve Solution The shape of the normal curve is bell shaped (graphically ) The curve has a single peak thus it is unimodel. The mean of a normally distributed population lies at the centre of its curve. Because of the symmetry, the median (Positional average) a mode (concentration of frequency) also lies at the centre. Thus in normal distribution mean, median and mode all coincide at zero..