AbstractThe mean annual range of temperature, and the standard deviation of hourly temperatures around the annual mean were compared for several dozen stations differing greatly in latitude and continentality. The two measures of dispersion display a linear relation, and a straight-line equation fitted by least squares allows the standard deviation to be computed from the range with a standard error little greater than I deg F., leading to the suggestion that frequencies and extremes can be estimated with sufficient accuracy for some purposes by starting with data limited to the means of the warmest and coldest months of the year.Examination of error patterns showed that standard deviations observed in continental stations are larger, and those in marine exposures smaller, than computed from the mean annual range. The departures are consistent with the response of the standard deviation to scatter caused by short-term fluctuations lost in monthly means. The standard deviation is thus the more accurate measure of dispersion, and its use in indices of continentality and the like is suggested. Errors did not increase progressively with the range, however, which led to examination of variance.Decomposition of the equations expressing variance in terms of the range show 1) the input of a sine wave relatable to the annual march of temperature, and 2) a term giving the dispersions stemming from the daily range of temperature plus irregular fluctuations. The growth of the first term relative to that of the second explains the linear relation seen in the scatter diagram initially plotted, and also sheds new light on comparative temperature regimes. If seasonal differences are slight, temperature variability must relate mainly to the daily cycle and whatever irregular fluctuations may be present, but where the mean annual range increases to much more than 20 deg (F), all stations in the sample agreed in showing the annual march of temperature the chief contributor to the variance of hourly temperatures around the annual mean.