Through examining the product of the mathematical variance of intensity with respect to time and frequency, we arrive at a temporal characterization of laser pulses through parameters for pulse duration, group delay dispersion and temporal form. These statistics, which are sufficient to predict subsequent pulse behavior, are recoverable in a simple experiment, measuring the two-photon-induced photocurrents in three nonlinear diodes. With only two photodiodes, we demonstrate that pulse durations as low as several tens of femtoseconds can be easily measured in a single shot if the usual assumptions of pulse form and dispersion are made as in the more difficult autocorrelation setup.