  Traditional forms of quantum uncertainty relations are invariably based on
the standard deviation. This can be understood in the historical context of
simultaneous development of quantum theory and mathematical statistics. Here,
we present alternative forms of uncertainty relations, in both state dependent
and state independent forms, based on the mean deviation. We illustrate the
robustness of this formulation in situations where the standard deviation based
uncertainty relation is inapplicable. We apply the mean deviation based
uncertainty relation to detect EPR violation in a lossy scenario for a higher
inefficiency threshold than that allowed by the standard deviation based
approach. We demonstrate that the mean deviation based uncertainty relation can
perform equally well as the standard deviation based uncertainty relation as
non-linear witness for entanglement detection.
