[Correction of the mean birth weight calculated from a frequency distribution (Japan, single births, 1969-88)]

Recently the mean birth weight (MBW) of Japan is on the decrease. This phenomenon started in 1976 and continues up to the present as of 1988. Various factors accounting for this phenomenon have been considered and discussed by several researchers. They were interested in social, cultural and economic factors as well as factors influencing community health status. Although the above factors seem to be important, one problem connected with calculation of MBW is worth discussing. The MBW was calculated from a frequency distribution because of a limitation of the source material. The accuracy of calculation of statistics from a frequency distribution depends on the assumption that few frequencies fall on boundaries, but birth weight measurements are apt to fall on figures having 0 at the end because of the properties of weighing scales. Suppose that the exact weight of an infant is 2996g. If his weight is read to the nearest figure having 0 at the end by rounding, it is recorded as 3000g on the birth certificate. Then, in a frequency distribution whose class interval is 500g, his weight is treated as 3250g in calculation of the mean. But some improvements of the methods of weighing, for example, utilization of a scale displaying a digital value of weight may result in a greater chance that his weight is recorded as 2996g. Then, in the same frequency distribution, his weight is treated as 2750g in calculation of the mean. Therefore, an improvement of the method of weighing produces the phenomenon that MBW decreases even if all the original birth weights did not change. Exact relative frequency, recorded as just 2500g, that is mentioned secondarily in the Vital Statistics of Japan has been decreasing consistently since 1969. This year is the oldest in the above source having frequency distributions of single birth infants. This fact shows that methods of weighing have been improved as the years pass. In this paper we tried to correct MBW by using the relative frequency recorded as exactly 2500g. Two kinds of widths where rounding would be executed were estimated from a frequency polygon. We obtained the following results. 1) The correction equation is represented as ld approximately; where l is a class interval (500g in this paper) and d is calculated by d = Q/(pa + pa+1 + Z) as a mean value in a certain sense and by d = 2Q/(pa + pa+1 + Z) as a maximum value.(ABSTRACT TRUNCATED AT 400 WORDS)