If i execute: "SELECT CAST(AVG(km_gelaufen) *AS REAL*) FROM laufdaten" the known problem of integer only shows up again.

BUT:

If i execute this "SELECT CAST(AVG(km_gelaufen)  AS REAL) FROM laufdaten " in SQliteStudio it works as it should.

Ok then it is clear that SQLite produces result as expected

Is DBgrid or Zeos Access components  the culpit? I don't know.

Do you use Zeos components not SQLdb (TSQLQuery)?
Can you test datatype of TField created at runtime?
For example place somewhere after dataset is Open-ed something like: ShowMessage(Fieldtypenames[Query1.Fields[0].DataType]);

L.
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