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I work in the finance field and I am looking at average balances on bank statements balances. When I have more than 1 bank statement I need to reflect the overall average balance between the accounts. I am not clear on whether the average balance from each account should be added together or averaged.

Avg. Bal Bank Acct #1: \$14,973

Avg. Bal Bank Acct #2: \$8,652

Total: \$23,625 - Should this be used for the average balances or

\$23,625 /2 = \$11,813 ?

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  • $\begingroup$ What does the average balance from one account mean? Is it the average over a month? $\endgroup$ – ShreevatsaR Jan 10 '14 at 19:33
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You can multiply them, too (though what square dollars mean, I don't know). Probably you want to add them together, which will give the average of the total of the accounts over the month. This is the average amount of money you had in total.

multiply them too

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  • $\begingroup$ Nice One!! The financial world is full of numbers like this , In the name of reconciliation from different systems of data, I go crazy every day. Thanks for your humor. $\endgroup$ – Satish Ramanathan Jan 10 '14 at 20:28
  • $\begingroup$ +1: it's impressive when you can find a cartoon which hits the nail so squarely on the head. $\endgroup$ – Pete L. Clark Jan 11 '14 at 4:05
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The word average means the second thing: the average of two numbers $A$ and $B$ is $\frac{A+B}{2}$, so in your case the average balance would be $\$ 11,813$, yes. (Well, actually it is $\$ 11,812.50$.)

However, that answer only goes as far as the meaning of the term. A better question is: for what you are trying to do, is it more meaningful to take the sum $A+B$ or the average $\frac{A+B}{2}$? That depends on what you're trying to do -- you didn't provide any more information -- but at least for me, if I have two bank accounts, it is the total amount of money which is more important than the average amount of money. In fact, I could hardly think of a more useless statistic for my purposes than the average amount of money in all my accounts.

Added: I just noticed that the two numbers you provided are already averages. This makes your question even less possible to answer purely mathematically. Really you are telling us: "I have two numbers $A$ and $B$, and I need to combine them in some way into one number. Should I do $A+B$ or $\frac{A+B}{2}$?" Answer: from a mathematical perspective, we don't know: it depends entirely on what you are trying to do. It sounds like what you were told was not clear enough, and you should ask again.

It is possible that someone with more experience working in a finance field would be better able to figure out what you are trying to do from your description, so you might have better luck on a different site, but I suspect that even a finance expert would find your question impossible to definitively answer.

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It depends on the type of analysis you do. If you have average balances of two accounts from two banks, and your analysis requires to find the aggregate, then you have to sum it. But if you are looking to report the average of the two accounts for some end analysis, then average of average is not a bad idea.

Thanks

Satish

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  • $\begingroup$ This seems to be equivalent to my answer, except that you point out that the word "aggregate" means "sum". Maybe that will be helpful to the OP. $\endgroup$ – Pete L. Clark Jan 10 '14 at 19:42
  • $\begingroup$ No problem, I am a financial analyst with math as my hobby, FDIC reports aggregate of average balances of all financial institutions for different type of loans, deposits and others while industry averages are calculated by the principle of average of averages $\endgroup$ – Satish Ramanathan Jan 10 '14 at 19:47
  • $\begingroup$ Right, I am a mathematician, and to me what you are saying is "Sums are computed by adding and averages are computed by averaging." I agree! Are you saying that the choice of whether to record $A+B$ or $\frac{A+B}{2}$ may in fact be a judgment call on the OP's part? (Of course, if s/he says what he is doing and there are always two accounts, then I don't see how anyone could complain. It's like wondering whether you should report your age or when you were born.) $\endgroup$ – Pete L. Clark Jan 10 '14 at 19:53
  • $\begingroup$ Good one, My answer might seem very obvious, I would have to agree with your comment about what the OP intends to do with these numbers ( end analysis)!!! $\endgroup$ – Satish Ramanathan Jan 10 '14 at 19:57

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