How do I calculate this

Hi there.
Please can you help me with the following problem. Lets say I have a group of cats.The group is 100.
2 cats eat 1 mouse per day
10=2
10=3
3=5
20=50
50=100
5=7
The average amount of mice eaten would be 27. But if I multiply this with the number of catsI get 2700 mice. This is not right. If I just add the numbers I need to by 6102 mice.
Now I dont want to add but at the same time have a working number in that kind of distribution.( lets say I buy another set of cats with similar feeding patterns. So I need a number which represents that.
Does that make any sense? Is there a formula? And is there a formula in Excel?
Thank you

I'm not exactly sure what you're asking. Are you looking for the mean of that set? If you want the mean, you can use this formula (assuming your data is in columns A and B):

=SUMPRODUCT(A1:A7,B1:B7)/SUM(A1:A7)

Mathematically, this is a weighted average of the equation ∑(#Cats * #Mice/Cat) / ∑(#Cats)

This simplifies to ∑(#Mice)/∑(#Cats), but you don't need to sum up every individual cat--you can take advantage of the fact that you have only 7 unique feeding patterns and do the calculation based on those 7 groups, rather than each of the 100 cats separately.

Hopefully this helps. Again, I wasn't exactly sure what you were asking.

Are you taking into account when you say that 10 cats eat 3 mice that that is 30 mice so you really need to add 1+1+2+2+2+2+2+2+2+2+2+2+3+3+3+3+3+3+3+3+… and so on