Theoretical expression of the mean birth weight and the standard deviation in frequency tables with various number of...

Using the birth weight frequency table with 500 g intervals and 10 classes (less than or equal to 999, 1000-1499,..., 4500-4999, 5000 less than or equal to) as a standard table (0 method) and creating 8 kinds of modified frequency tables (a,..., h method) by integrating the lower and/or upper classes in the standard table into neighboring classes, we assessed the differences of both the mean birth weights (MBW) and the standard deviations (SD) between 0 method and 8 kinds of methods (a,..., h method) from the aspect of frequencies belonging to the integrated classes. The equations expressing the differences of MBW were obtained as a function of relative frequencies belonging to the integrated classes. Although the differences of the variances can be exactly expressed as a function of three kinds of variates, namely the relative frequencies, the number of live births and MBW by the corresponding modified method (or 0 method), the differences of SD can be obtained only as approximations of the above function by adding SD by the corresponding modified method (or 0 method). Examining the degrees of approximations at the prefectural, the health center and the city-town-village levels, we were able to recognize good approximation by simple forms with the relative frequencies and SD by the corresponding modified method (or 0 method). We pointed out that these formulas were useful for transforming MBW and SD by 0 method into those by the modified methods and for assessing the differences of MBW and SD.