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Default Summing a range within a range

I need the formula that will sum a range within a range. Example: the primary
range consists of the following numbers: 1,2,3,4,5,6,7,8,9,10 and I need to
know how many numbers are 3 and <8. First I need to know the sum ot the
qualifying numbers; second I need to know how many items there are.

Stumped and exhausted...anyone's help will be greatly appreciated!
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