The error sources were analyzed from the measurement of the Kubler Index. A statistical method was proposed for the error calculation of full width at half maximum (FWHM) of X-ray diffraction peaks from the "Strip-chart" diffractometer, while formulas describing the relations a-mong the intensity, shape and measuring conditions were used for that of "Digital" diffraction peaks. A special discussion is given for the data smoothing-an operation could be used for "Digital" peaks--in which the principle of error production and general trend of smooth operationare described. It is believed that these equations and principles could be also used for the calculations of any other peak parameters and digital spectrum analyses.