Cumulative frequency data to individual frequency approximation?

Factual Questions
1

I admit it, my rusty old math has rusted out completely. I’ve got some cumulative frequency data that I’d like (for the sake of nothing but curiousity) to derive approximations of discrete frequency as if it were a smooth curve on points that aren’t trivially implicit in the cumulative frequency.

It looks approximately gaussian but the median and mean do not coincide, it’s absolutely bounded on the lower end and has an extended tail on the higher end.

2

You lost me at, “…trivially implicit in the cumulativel frequency.”

Do you mean you’d like to use generalized data to address an individual case?

3

I just want to play at interpolation. This is not any sort of serious work, just idle curiousity.

4

Yeah, I have to admit I can’t catch your meaning. When you say “cumulative frequency data”, I think of something like:



bin   value
---   -----
 1      2
 2      6
 3     14
 4     16
 5     20
 6     21
 7     23
 8     27

which, in histogram form, might look like:



    |                     ____
 25 |                     |  |
    |                  ___|  |
 20 |            ___---      | 
    |            |           |
 15 |      ___---            |
    |      |                 |
 10 |      |                 |
    |   ___|                 |
  5 |___|                    | 
    |_________________________
      1  2  3  4  5  6  7  8

Note that since this is a cumulative distribution, it is monotonic. So if your distribution is peaked, it isn’t cumulative. Did you start with a cumulative distribution, like the above, and create from it the underlying “absolute” frequency distribution (or in different language, the underlying discrete probability density function)? Is that what you found to be Gaussian-like? Are you wishing simply to rebin (i.e., create an approximation of how the discrete distribution would have looked were the original data binned differently)?

In what form are your data?