Deviation with intervals

I'm having an issue finding a way to distribute numbers in even intervals for any set of given data.

With Standard Deviation, it's easy to find 3 even intervals:

1. Over the average + standard deviation
2. Under the average + standard deviation
3. Somewhere in between both.

Basically this is like a Normal distribution, but simplified to the 3 classic groups, but what I cannot figure out, is how to divide this into some extra even intervals (my question is to know exactly how I could have an even number of elements in each interval)

For example, if I have 20 elements and I want 5 intervals, this could fit something like:

A) 2 elements in the first group
B) 3 elements in the second group
C) 10 elements in the third group
D) 3 elements in the fourth group
E) 2 elements in the last group.

Always the elements in each group have to be compensated with the other group in the other side, just like in a normal distribution.

I need to find the formula to be something like:

Over the Average + X = First group
Average + Y = Second group
Average - Y = Fourth group
Average - X = Fifth group
In between Second and Fourth = Third group

Any ideas on how I can identify the X and the Y for any given number data set like in a normal distribution?

I've tried to explain this the best I could, I'm sure I have studied this ages ago, but I can't remember any solution to this pattern. Maybe someone that works more fluently with statistics can help me out :)

Thanks in advance.
It seems to me that you're asking about the concept of area under a distribution curve, and wish to partition that into sections of equal area.