This post stems from this Question to which the author has never taken the time to give any answer whatsoever.

To help the reader understand what this is all about, I reproduce an abriged version of this question

The data the author refers to is a collection of decimal numbers.

The term "histogram" has a very well clear meaning in Statistics, without entering into technical details, let us say an histogram is an estimator of a Probability Density Function (continuous random variable) or of a mass function (discrete random variable), see for instance Freedman & Diaconis.

The expression "cumulative histogram" is more recent, see for instance Wiki for a quick explanation. Shortly a cumulative histogram can be seen as an estimator of the Cumulative Density Function (CDF) of a random variable the sample at hand is drawn from.

I said this expression is quite recent (it seems to come from the image processing field) for it already exist for long the concept of ECDF (Empirical Cumulative Distribution Function) has been around for a long time and is a true estimator of the CDF above.
Personally I am always surprised that someone wants to draw a cumulative histogram (which necessarily contains approximations: anchors, number of bins, binwidth selection method, ...) whereas the ECDF is an objective approximation-free information which is just as easy to get and plot.

Anyway, I have done a little bit of work arround the OP's question whiwh ended in a procedure named Hodgepodge (surely not a very explicit name but I was lacking inspiration) which enables plotting (if asked) several informations in addition to the required cumulative histogram:

• The histogram of the raw data for the same list of bin bounds.
• The kernel density estimator of this raw-data-histogram.
• The ECDF of the data.
   

Here is an example of data

and here is what procedure Hodgepodge.mw  can display when all the graphics are requested