Help putting this into a mathematical equation

Question

I have a list of names like the following within group:

Western Group 1
John = 2
Charlie = 3
Hatty = 7
Pete = 4

Western Group 2
Jane = 6
Peter = 5
Dave = 4
Lisa = 4

Eastern Group 1
Dae = 1
Awa = 1
Flad = 6
Daw = 3

Eastern Group 2
Feda = 2
Caveer = 6

The number of groups I can have vary.

My Forumla is like this:

Average Western Group = ((Total of Group 1 / Number of names within group 1) + (Total of Group 2 / Number of names within group 2)) / Number of groups

E.g. in the sample data I've provided it would output the following:

Average Western Group = ((2+3+7+4 / 4) + (6+5+4+4 / 4))/ 2

Then do the same again for the Eastern Groups.

The required value is the median value between Average Western Group and Average Eastern Group like so:

Required Value = (Average Western Group - Average Eastern Group) / 2 + Average Eastern Group

The issue I'm having is that I need a single mathematical equation where I won't know how many groups there will be and I won't know how many names there will be in a group.

I do realise this question is a little odd but is there a way to put this into a single real mathematical equation? I'm wrecking my brain over this. I'm sure its simple but I seem to have hit a brick wall at the moment.

Answer 1

Given a line such as this:

Average Western Group = ((Total of Group 1 / Number of names within group 1) + (Total of Group 2 / Number of names within group 2)) / Number of groups

You can make it universal by substituting in a variable for a group. For example, name terms n1, n2, n3 ... infinitely. The Western group 1 would = (n1+n2+n3...)/number(n)

Hope this helps