Hi Jason,
That formula never fails to stir the possoms.
I retired for the evening straight after posting my reply and missed
all the action.
JE was kept pretty busy while I was snoozing!
It's good to get JE's opinions on the workings of that formula. I'm
sure this thread will remain bookmarked on my computer for quite some
time.
I first saw the formula last Sept when Bob Phillips replied to a
similar request.
My immediate reaction was disbelief and confusion so I started a new
thread
"Can anybody explain to me how Bob Phillips' unique record counter
work?"
in microsoft.public.excel.programming
To save you going to the trouble of doing a search I've pasted Bob's
responses below.
Bob's website, xldynamic, has heaps of other SUMPRODUCT examples worth
looking at.
Ken,
Spookily, Richard Buttrey asked the same question this morning.
Here is my reply re-posted
Let's start by defining the range A1:A20 to talk specifics.
Bob,John,Bob,Bob,John,John,Bob,Bill,Bill,Max
or data in just A1:A10
The basic formula to count unique items is
=SUMPRODUCT(1/COUNTIF($A$1:$A$10,$A$1:$A$10))
The COUNTIF($A$1:$A$10,$A$1:$A$10) part of the formula builds an array
of
the number of occurrences of each item, in this
case{4;3;4;4;3;3;4;2;2;1}.
As can be seen, each occurrence of the repeated value is counted, so
there
are four occurrences of Bob in the array. There will always be the same
number of occurrences of value as the count of that value, unless two
or
more items are repeated the same number of times, in which case it will
be
some multiple of that count.
Thus the item that is repeated 4 times has 4 instances of that count,
dividing 1 by the count of 4, gives 0.25 4 times. The full array of
values
is
{0.25;0.333333333333333;0.25;0.25;0.333333333333333;0.333333333333333;0.25;0
.5;0.5;1}.
The item that repeats 4 times sums to 1. The item that repeats 3 times
also
sums to 1. It should be clear from this that every value works in the
same
way and sums to 1. In other words, 1 is returned for every unique item.
The
sum of these values becomes the count of unique items.
As our test range is A1:A20, and some of the items in A1:A20 are blank,
extending this formula to A1:A20 would return a #DIV/0! Error.
The reason for the error is blank cells in the full range A1:A20. Each
blank
cell returns a 0 value from the COUNTIF formula, which gives the
#DIV/0!
Error when divided into 1.
The solution to this is to force it to count the empty cells as well,
and
not return a zero. Adding &"" to the end of the COUNTIF formula forces
a
count of the blanks.
This addition on its own removes the #DIV/0! error, but will cause the
blanks to be counted as a unique item. A further addition to the
formula
resolves this by testing for those blanks. Instead of dividing the
array of
counts into 1 each time, adding the test creates an array of TRUE/FALSE
values to be divided by the equivalent element in the counts array.
Each
blank will resolve to FALSE in the dividend array, and the count of the
blanks in the divisor array. The result of this will be 0, so the
blanks do
not get counted.
--
HTH
Bob Phillips
(Bob,
Thanks for that, it's going to take me a while to work through it. It's
easily the most amazing bit of excel wizardry I've ever seen. Is it
your own invention?
Ken Johnson)
I wish I could lay some claim to that but I cannot. It is doubtful that
anyone can claim these things absolutely as so many contribute to their
evolution. I first saw it in a more simplistic form
=SUMPRODUCT(1/COUNTIF(A1:A20,A1:A20)
and it has evolved over the years to what I showed that day.
There are better ones out there IMO, although that does have the appeal
of
brevity. I saw one from Domenic a few weeks back that sums in
non-contiguous
cells that I really liked
=SUMPRODUCT(--ISNUMBER(MATCH(COLUMN(C1:N1)-COLUMN(C1)+1,{1,3,6,8,12},0)),--(
C1:N1>=1))
This sums C1,E1,H1,J1,N1 only. I had a solution to this problem, but
not as
elegant.
Here is one of mine for extracting the numbers from a delimited string
and
sum them. So if A1 contains 1,12,123 it will get the 1 and 123 out and
sum
them
=SUMPRODUCT(--MID(A1,FIND("~",SUBSTITUTE(B1&A1&B1,B1,"~",ROW(INDIRECT("1:"&L
EN(A1)-LEN(SUBSTITUTE(A1,B1,""))+1)))),
FIND("~",SUBSTITUTE(B1&A1&B1,B1,"~",ROW(INDIRECT("2:"&LEN(A1)-LEN(SUBSTITUTE
(A1,B1,""))+2))))-
FIND("~",SUBSTITUTE(B1&A1&B1,B1,"~",ROW(INDIRECT("1:"&LEN(A1)-LEN(SUBSTITUTE
(A1,B1,""))+1))))-1))
If you think that all this is useful, take a look at
http://www.xldynamic.com/source/xld.SUMPRODUCT.html
--
HTH
Bob Phillips
That should keep you busy for a while Jason.
Ken Johnson
It also sheds some light on one of Domenic's previous posted