How do I rank these leaving groups?

[Delta what]

1. The problem statement, all variables and given/known.
Rank the following leaving group in order of increasing ability to leave?
A) H2O B) NH2 C) OH D) I E) NH3

Homework Equations

Also not entirely sure the order of H2O and NH3. What should I be looking for to answer this portion of the question?
Also my study group believes the better leaving group is a halogen. Is that correct?

3. The Attempt at a Solution
I think the answer is
B<C<D<A<E
My study group thinks it may be B<C<A<E<D

 

[fresh_42]

I'm not good in chemistry and don't know what "leaving" here means. Is it this:
https://en.wikipedia.org/wiki/Bond-dissociation_energy?

 

[Delta what]

I'm not good in chemistry and don't know what "leaving" here means. Is it this:
https://en.wikipedia.org/wiki/Bond-dissociation_energy?

No it is not. What you had linked to is in regards to the bond dissociation of a molecule when creating, what I believe to be, a free radical. Or when the two substances dissociated from each other leave with an unpaired electron. A leaving group in my question deals with one that leaves with a charge or in the case with H2O and NH3, had a charge when attached but when it leaves the two groups have a zero charge.
Here is a wiki article fresh_42 on the leaving group.
https://en.wikipedia.org/wiki/Leaving_group

 

[Jen1114]

I believe that the most effective leaving group is going to be the weakest base. So in this case the best way to figure it out would be to look at a table of pka values and rank them in order of which pka values are the lowest.

 

[Delta what]

 

[Delta what]

I got that image from http://www.masterorganicchemistry.com/2011/04/12/what-makes-a-good-leaving-group/
So from that graph and using the pka values the order should be b<c<e<a<d.
It is very odd to me that a charged halogen is a better leaving group than a zero charged NH3 or H2O. My reasoning for why I think this is odd is because I tend to think the stability or ΔG is greater (G is lower in number) in the H2O and NH3 and the ΔG for the I^- is to a lesser extent (or higher number in free energy). Due to the lower energy of the H2O and NH3 they would be a better leaving group. I know that I am wrong in this thinking but I am I totally off base here? Maybe I have the ΔG values incorrect and the halogen is more stable? Other than the pka values what would be a good way to develop my intuition as to why these halogens (except F) are better at leaving? Thanks!