The results of studies of atmospheric pressure in the Arctic region of Russia in the period from 1948 to 2008 are presented. The analysis of the climatic seasonal variation of the atmospheric pressure fields is carried out. As the main research method, the probabilistic and statistical analysis of the time series of the pressure field 60 years long at fixed points in the region of the Arctic zone of Russia was used. In total, about 90,000 daily (in six-hour increments) pressure values were examined. On the basis of these data, a climatic seasonal variation was constructed as an averaging of the values of a given time series at each point in space and for a fixed date. The characteristics of the seasonal course, its amplitude and phase have been studied. These characteristics were analyzed and their geophysical interpretation was carried out. In particular, the minimum and maximum values ​​of the series were determined for the entire region and the time series of these characteristics were constructed. It is shown that the deviation is asymmetric, this is an unobvious research result. For the maximum and minimum, the best approximations were constructed, and these approximations were tested by known methods of statistical analysis, including maximum likelihood, least squares and goodness of fit methods (tests), in particular, the χ²-criterion. The conducted research has applications both purely physical (allows to explain the nature, genesis and distribution of large-scale atmospheric formations in a climatic year) and prognostic (allows understanding and tracking trends in climate, as well as quantitatively assessing the scale and variability of large-scale atmospheric processes). Numerical calculations were performed on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.