Question: Count and sum values between 1 and 3 in column A

Answer: Count numbers between 1 and 3.
=SUMPRODUCT((A1:A15>=1)*(A1:A15<=3))
A1 is above or equal 1? Yes. A1 is below or equal to 3? No. (1*0=0)
A2 is above or equal 1? Yes. A2 is below or equal to 3? Yes. (1*1=1)
A3 is above or equal 1? No. A3 is below or equal to 3? Yes. (0*1=0)
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The sum of all of these calculations (bold) will give you the counted number.

Sum numbers between 1 and 3.
=SUMPRODUCT((A1:A15>=1)*(A1:A15<=3)*(A1:A15))
A1 is above or equal 1? Yes. A1 is below or equal to 3? No. (1*0*8=0)
A2 is above or equal 1? Yes. A2 is below or equal to 3? Yes. (1*1*2=2)
A3 is above or equal 1? No. A3 is below or equal to 3? Yes. (0*1*0=0)
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The sum of all of these calculations (bold) will give you the sum of the counted numbers.

SUMPRODUCT(array1;array2;...)
Returns the sum of the products of the corresponding ranges or arrays