Vienna, 1908-1909: (Source: R. van Mises, "Probability, Statistics, and Truth") month total births proportion girls Jan .4777 Feb (average .4875 Mar was 3903 .4859 Apr per month) .4754 May .4874 Jun .4864 Jul .4813 Aug .4787 Sep .4895 Oct .4797 Nov .4876 Dec .4859 Jan .4857 Feb .4907 Mar .5010 Apr .4903 May .4860 Jun .4911 Jul .4871 Aug .4725 Sep .4822 Oct .4870 Nov .4823 Dec .4973 Total proportion girls: .4857 Observed standard deviation of proportion girls: .0064 Expected s.d. of proportion girls: sqrt((.486)(1-.486)/3903) = .0080 95% conf. interval for observed s.d. (based on chi^2 with 23 d.f.): (.006, .010) (observed s.d not sigificantly different from binomial model) California: (Source: State of California, Department of Health Services, birth records) year girl births total births proportion girls 1982 209,674 429,631 .4880 1983 212,700 435,722 .4882 1984 218,421 447,394 .4882 1985 229,843 470,816 .4881 1986 1987 244,966 503,376 .4866 Total proportion girls: .4878 Observed standard deviation of proportion girls: .0006 Expected s.d. of proportion girls: sqrt((.488)(1-.488)/450,000) = .00075 95% conf. interval for observed s.d. (based on chi^2 with 4 d.f.): (.0003, .0012) (observed s.d not sigificantly different from binomial model) United States: (Source: Statistical Abstract of the United States) year girl births total births proportion girls 1975 1,531,000 3,144,000 .4870 1976 1,543,000 3,168,000 .4871 1977 1,621,000 3,327,000 .4872 1978 1,624,000 3,333,000 .4872 1979 1,703,000 3,494,000 .4874 1980 1,760,000 3,612,000 .4873 1981 1,769,000 3,629,000 .4874 Total proportion girls: .4872 Observed standard deviation of proportion girls: .00018 Expected s.d. of proportion girls: binomial s.d: sqrt((.487)(1-.487)/3,300,000 = .00028 round-off error: relative error in numerator: 1/(sqrt(12)*1,650) = .00017 relative error in numerator: 1/(sqrt(12)*3,300) = .00009 absolute error of ratio: .487*sqrt(.00017^2+.00009^2) = .00010 total error: sqrt(.00028^2 + .00010^2) = .00029 95% conf. interval for observed s.d. (based on chi^2 with 6 d.f.): (.00013, .00045) (observed s.d not sigificantly different from binomial model) Simple summary (to show sqrt(n)) behavior: data set binomial N sd(x/N) sqrt(N)*sd(x/N) theoretical value Vienna 3903 .0064 .40 .50 California 450000 .00067 .45 .50 U.S. 3300000 .00018 .32 .50 (Also, the means from the three samples are not quite statistically significantly different from each other.)