Calculate average over variable range

I'd like to calculate an average over a variable range. In col.A there are grades from A4:A21. In col.C there are the values for the start row of the range and in col.D the values for the end row of the range.

For instance the value in C4=4 and D4=9. In cell F4 I want the average calculated over A4:A9.

Value in C5=10 and D5=15. In cell F5 I want the average calculated over A10:A15.

etc.

I tried to make it work with the average function combined with offsett, but to no avail. Can somebody please help me.

Use INDEX

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