The quality of geophysical measurements may be obtained from statistical studies in which the probable error of a single observation is estimated. Since many geophysical functions, when plotted in profile form, resemble smooth mathematical curves upon which "static" caused by random errors is superimposed, it is possible to substantially remove the measured function from the errors through the construction of difference tables. Higher orders of differences consist primarily of systematic combinations of individual errors. When a function, u, is observed at equally spaced points, the probable error of a single observation may be obtained from the equation [.........] where u is the measured function, m is the order of the differences,n is the number of measurements, and the K's are the binomial coefficients of the order, m. Application of the method to seismic and gravity profiles results in probable errors that are consistent with those obtained from the studies of basic data acquired in the field. The method may also be used in many other measurements in the field and laboratory.