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Default Just a brain teaser (for the math guys)

Okay, so I've managed, with the help of those here, to make a pretty
impressive spreadsheet. But I ran into an interesting problem and maybe you
guys can help me understand it.

Just so you know, I've figured out another way to get my answer though I'm
not 100% sure it's the correct answer, this isnt a Help Me Please!!!
question. Just a hmmm, thats weird question.

I have a list of 35 annual training requirements. The title of each
requirement has its own column. The very first column has a list of about 230
names and each row should have the date in which that person completed the
requirement. Well, not every person has every requirement so I need a
percentage of how many people have completed any given requirement, by
section and total.

I did this by =COUNTA(H3:H21) at the bottom of each column and then below
that = H22/ 19 as an example. 19 names divided by how many dates I have in
that column, or visa versa. Somethings divided by something; Im too tired
to think.

Okay, because I have 11 different work sections, I have 11 different
worksheets, each one with 35 columns for the requirements. Now it used to be
that I had all the names together in one long list, but I figured it would be
easier to separate them by work section. Boy was I wrong! But its been fun
learning all this so its no biggy.

Anyway, I have 11 different Operational Risk Management (ORM) columns,
each with its own percentage of whos completed the training. But I also
needed to know a total percentage. Each of those columns will tell me the
percentage for that section, just for those 7 to 20 people, depending on the
section. But I also need to know what that percentage is for everyone
combined.

Now I thought that I could use this fancy function,
=SUM((ACAD!AY7+ADMIN!AY23+'S-3 OPS'!AY14+FACM!AY29+MESS!AY30+'S-4
LOGS'!AY10+MT!AY21+SUPP!AY23+FS!AY43+COMM!AY16+UTG !AY54)/ 11)

Well the AY is the column for ORM, the numbers are different because the
number of people are different for each section. Now heres the important
thing to remember, AY7, AY23, AY14 and so on, those correspond to the row
that tallies the percentage for each section. Youll notice that I divide all
that by 11, which gives the total for everyone.

Well, you have your answer, you might say. BUT

When I went back and did it manually by numbers alone, in other words, just
to check the math, I counted all of the people who completed the requirement
and then divided that by 230 and I got a different number, a different
percentage. Thats what this is all about. Why am I getting a different
number?

Whatever the answer, I decided I trusted the numbers alone approach more and
redid all my equations or whatever theyre called. But I was wondering if a
math genius here might tell why the answers are different. My thought was
that the percentages by section were conflicting because each section has a
different number of people, if that makes any sense. The odd thing is, there
is only a few points difference between the two different answers, in some
cases about .05 and at most 6.

I know that this is a bit wordy but I wanted to paint a clear picture AND I
know that this is more of a math question and has less to do with Excel. But,
in my defense, it started because of Excel, so there.

Thank you much for your time. Hopefully youll consider this a break from
the normal questions.

 
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