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Intuitively, one would expect a more skillful forecast if predicting weather averaged over one week instead of the weather averaged over one day, and similarly for different spatial averaging areas. However, there are few systematic studies of averaging and forecast skill with modern forecasts, and it is therefore not clear how much improvement in forecast performance is produced via averaging. Here we present a direct investigation of averaging effects, based on data from operational numerical weather forecasts. Data is analyzed for precipitation and surface temperature, for lead times of roughly 1 to 7 days, and for time- and space-averaging diameters of 1 to 7 days and 100 to 4500 km, respectively. For different geographic locations, the effects of time- or space-averaging can be different, and while no clear geographical pattern is seen for precipitation, a clear spatial pattern is seen for temperature. For temperature, in general, time averaging is most effective near coastlines, also effective over land, and least effective over oceans. Based on all locations globally, time averaging was less effective than one might expect. To help understand why time averaging may sometimes be minimally effective, a stochastic model is analyzed as a synthetic weather time series, and analytical formulas are presented for the decorrelation time. In effect, while time averaging creates a time series that is visually smoother, it does not necessarily cause a substantial increase in the predictability of the time series.