Summing Only the Largest Portion of a Range

Christian has a range of 18 cells that contain values. He would like to find the sum of the 12 largest values in that range and wonders how to accomplish the task.

There are several ways you can approach this problem. You could, for instance, filter the values so you only have the top twelve values, and then sum those. Other approaches involve using additional columns to store intermediate values, but I'll assume that you would prefer an approach that didn't use additional columns.

To start, let's assume that your range of 18 cells is A1:A18. You can use the LARGE function to find the largest values. For instance, using this formula would find the second-largest value in the range:

=LARGE(A1:A18,2)

It is the function's second parameter that specifies which largest value, in order, you want. Thus, you could find out the sum of the 12 largest values by using a formula such as this:

=LARGE(A1:A18,1)+LARGE(A1:A18,2)+LARGE(A1:A18,3)+LARGE(A1:A18,4)
+LARGE(A1:A18,5)+LARGE(A1:A18,6)+LARGE(A1:A18,7)+LARGE(A1:A18,8)
+LARGE(A1:A18,9)+LARGE(A1:A18,10)+LARGE(A1:A18,11)+LARGE(A1:A18,12)

There are shorter formulas you can use to accomplish the task, however. For instance, you could simply subtract the six smallest values from the sum of the range, in this manner:

=SUM(A1:A18)-SMALL(A1:A18,1)-SMALL(A1:A18,2)-SMALL(A1:A18,3)
-SMALL(A1:A18,4)-SMALL(A1:A18,5)-SMALL(A1:A18,6)

You can also, if you desire, use the SUMIF function to do a comparison of the values and sum them only if the criterion you specify is met. For instance, consider these two formulas:

=SUMIF(A1:A18,">="&LARGE(A1:A18,12))
=SUMIF(A1:A18,">"&SMALL(A1:A18,6))

The first formula will sum all the values that are greater than or equal to the twelfth largest value in the range. The second is similar in effect; it sums all the values that are greater than the sixth smallest value.

These two formulas work great if there are no duplicate values at the "boundary" established. If, however, there are more than one value that qualify as the twelfth largest or the sixth smallest, then the formulas won't return the sums you expect. In the first formula the sum will be too large (since all of the duplicate values are added to the sum) and the second formula the sum will be too small (since all of the duplicate values are excluded from the sum).

The way around this is to either go back to one of the earlier formulas (the ones that don't use SUMIF), or modify the SUMIF formula so that it takes the possibility of duplicate values into account:

=SUMIF(A1:A18,">"&LARGE(A1:A18,12))+LARGE(A1:A18,12)
*(12-COUNTIF(A1:A18,">"&LARGE(A1:A18,12)))

Perhaps the best formula to get the desired result places a twist on the earlier use of the LARGE function:

=SUM(LARGE(A1:A18,{1,2,3,4,5,6,7,8,9,10,11,12}))

This formula uses an array (the part within braces), but it is not an array formula. What it does is to use the array as the second parameter of the LARGE function, thus returning all twelve largest values. These are then summed and a single value returned.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (9420) applies to Microsoft Excel 97, 2000, 2002, and 2003. You can find a version of this tip for the ribbon interface of Excel (Excel 2007 and later) here: Summing Only the Largest Portion of a Range.