Spatial and temporal averaging of observational data is widely used in many problems of meteorology, hydrology and related sciences. Several averaging methods have been proposed by various scientists and are used on a regular basis to obtain data averaged in space orfand in time, to yield data which are less influenced by random factors than initial point data are. The significance of averaging meteorological fields has substantially increased nowadays in connection with the problem of global climate change. However important as such change may be, it is very small as compared with the natural variability of atmospheric fields. An accurate averaging is absolutely necessary in order to discover a small climate change signal on the background of strong natural variability that acts as a random noise in this context. It is highly desirable not only to determine the averaged values themselves, but also to estimate the accuracy with which these values are known. To evaluate the accuracy of averaging is not a simple task mainly because the initial point values are not independent from each other, and interconnections between them substantially influence the averaging accuracy.