point - How to interpolate missing data from neighbours in PostGIS?

I have a dataset with point data within a given country. Let's say my dataset looks somewhat like this:

tree_id | species | age | geom
------------------------------
   0    |   Ash   | null| ...
   1    |  Beech  |  70 | ...

   2    |   Ash   |  10 | ...
   3    |  Beech  |  70 | ...
   4    |  Beech  | null| ...
   5    |  Beech  |  60 | ...
  ...   |   ...   | ... | ...

As you can see the dataset has some missing data. For instance, tree_id 0 has no age. Therefore I would like to interpolate those missing values from a 100 meter radius.

I am looking for the mean of the species. The result should also include the number of sample trees used. A result table could then look like this:

tree_id | age_avg | samples
---------------------------

   0    |   11.8  |  113
   3    |   12.2  |   97
   5    |   50.7  |  272
  ...   |   ...   |  ...

Could you get me started with some PostgreSQL query code, please?