Mapping the standard deviation of values within a given proximity to a location

Question

I have scattered point data with a single attribute. How can I assign to a reference raster pixel, the mean and standard deviation of all points within radius r of that pixel?

I could buffer a point grid and iteratively compute this using python, but it feels like a common enough thing that there must be an out-of-the-box tool (I don't work with raster data much).

Image for clarity:

Answer 1

Conceptually, I was trying to gather 'Focal Statistics'. So, I accomplished something that approximates my end goal using the r.neighbors tool in the QGIS processing toolbox. Here is how I did it:

1. Rasterize the point data to be used as input
2. Create a constant raster to use as a reference (as an option, the r.neighbors processing tool can accept a raster that will dictate which cells to calculate statistics on, in my case, I want 100% coverage across a particular area, so constant raster works perfectly here)
3. Run r.neighbors with the point raster as the input and the constant raster as the reference. Configure the search pixel width and make the search area circular.