# Unable to get the correct answer - what am I doing wrong!?

Arithmetic and Geometric progressions.

### Unable to get the correct answer - what am I doing wrong!?

Hello,

I have two means (both of which are average antibody concentrations for a group of subjects calculated by multiplying all values and taking the nth root of this number, where n is the number of subjects with available data).

The first mean for group 1: 8985.
Group 1 is made up of 67 subjects.

The second mean for group 2: 7622
Group 2 is made up of 132 subjects.

I have been given the overall mean is 8056. However, I do not know how this number was arrived at. I have attempted the formula:

(67*8985)+(132*7622) = 1608099 / 67+132 = 8080.8995.

I don't understand where I am going wrong???
Guest

### Re: Unable to get the correct answer - what am I doing wrong

The "mean value" for a collection of "m" numbers is arrived at by dividing the total of the numbers by m.

Given the mean value, we can go back the sum (but not the original list of numbers) by multiplying by m.

The first collection, of 67 numbers, has mean 8985 so the numbers total 67(8985)= 601995.

The second collection, of 132 numbers, has mean 7622 so the numbers total 132(7622)= 1006104.

Altogether there are 67+ 132= 199 numbers with grand total 601995+ 1006104= 1608099 so the mean if all the numbers is 1608099/199= 8080.89949748743718592964824120. That is exactly what you have done and it looks like you have the correct answer. I have no idea where "8056" came from

HallsofIvy

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