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Dispersion measurement data from two sets of fiber cable lengths were employed to determine the histograms of slope and wavelength of zero chromatic-dispersion in concatenated single-mode fibers. We use a Monte-Carlo technique under two concatenating scenarios, depending on whether those fibers being concatenated are or are not manufactured by the same process. Results show that the variances of slope and wavelength of zero dispersion are inversely proportional to the number of fiber cable lengths being concatenated. The average and standard deviation of zero-chromatic dispersion wavelength changes less than 0.005 percent or 1 percent, respectively, when the actual dispersion slopes of individual fiber lengths being concatenated are replaced by random quantities distributed with uniformity within 0.08-0.1 ps/km . nm2.