  We investigate the lower bound obtained from experimental data of a quantum
state $\rho$, as proposed independently by G\"uhne et al. and Eisert et al. for
mixed states of three qubits. The measure we consider is the convex-roof
extended three-tangle. Our findings highlight an intimate relation to lower
bounds obtained recently from so-called characteristic curves of a given
entanglement measure. We apply the bounds to estimate the three-tangle present
in recently performed experiments aimed at producing a three-qubit GHZ state. A
non-vanishing lower bound is obtained if the GHZ-fidelity of the produced
states is larger than 3/4.
