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Averaging a big number of pixels within a several km radius

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I work with ArcMap software and now I have the aim to average individual pixels within a several km radius from daily data for at least 1 month. So I made the grid with 4 km step (the step size is not important for the question) and now I have to average pixels according to the described method. How do you think what the tool from ArcTools window I should use for this?


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