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I have a point layer with x,y,z coordinates with geothermal temperature data. This data should be related to a given vector layer of political communities. In order to analyse every single community to their temperature distribution according to the depth (min, max, mean, standard deviation).

I tried it with the Spatial data processing framework plugin "merge attributes by position" (not sure if its the right translation from German). With this I get the sum, min, max results for each community.

I would like to get all the temperature data within every single community, to have further possibilities of analysing the data.

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If I am understanding your question correctly, I think you should be able to merge the community with the x,y,z points. This would add an attribute onto the point file indicating which community it belongs to, which you could then use for further analysis.

For example if you have some points representing the temperatures within several communities represented as polygon, here the communities are called "A" and "B": example points and polygons

Using Vector>>Analysis Tools>>Join Attributes by Location, then select your point temperature layer as your Input layer, and the polygon community layer as your Join layer. I'm using QGIS version 3.0.1 but I think it's consistent for most recent versions.
example join dialogue box

This will add the polygon attributes to each point: Joined table

You can then sort or filter the points by the community.

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