Sum unique distinct numbers
The image above shows numbers in column B, some of these numbers are duplicates. The formula in D12 adds unique distinct numbers meaning the first instance of each number is added to the total, however, the duplicates are ignored.
Explaining formula in cell D12
If you want to examine the formula yourself then go to tab "Formula" on the ribbon and then click "Evaluate Formula" button.
This will show the calculation steps, one at a time. Simply click the Evaluate button to move to next calculation step.
Step 1 - Count each value in cell range
The COUNTIF function counts each value in the cell range and returns an array of numbers which shows the number of instances each value has.
COUNTIF(B3:B15,B3:B15)
becomes
COUNTIF({9;8;7;1;2;6;3;1;7;2;8;2;6},{9;8;7;1;2;6;3;1;7;2;8;2;6})
and returns
{1;2;2;2;3;2;1;2;2;3;2;3;2}.
Step 2 - Divide 1 with array
If a number has a duplicate then there are two instances of that value. Divide 1 with 2 and we get 0.5, now multiply that value with the number and we get the number to add to the total.
1/COUNTIF(B3:B15,B3:B15)
becomes
1/{1;2;2;2;3;2;1;2;2;3;2;3;2}
and returns
{1;0.5;0.5;0.5;0.333333333333333;0.5;1;0.5;0.5;0.333333333333333;0.5;0.333333333333333;0.5}
Step 3 - Multiply with numbers
The parentheses make sure that the order of calculation is correct.
(1/COUNTIF(B3:B15,B3:B15))*B3:B15
becomes
{1;0.5;0.5;0.5;0.333333333333333;0.5;1;0.5;0.5;0.333333333333333;0.5;0.333333333333333;0.5}*B3:B15
and returns
{9;4;3.5;0.5;0.666666666666667;3;3;0.5;3.5;0.666666666666667;4;0.666666666666667;3}
Step 4 - Add numbers
The SUMPRODUCT function is a better option than the SUM function, we don't need to enter the formula as an array formula now.
SUMPRODUCT((1/COUNTIF(B3:B15,B3:B15))*B3:B15)
becomes
SUMPRODUCT({9;4;3.5;0.5;0.666666666666667;3;3;0.5;3.5;0.666666666666667;4;0.666666666666667;3})
and returns 36 in cell D12.
Download Excel *.xlsx file
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