You are literally denying the law of identity. You probably shouldn't do that.
<obnoxious font punatively removed>
One of these things is not like the others,
One of these things just doesn't belong,
Can you tell which thing is not like the others
By the time I finish my song?
How does "all graphs are graphs" imply "all graphs are identical"? (It doesn't.)
Bzzzzt! Wrong again
Can you please explain what is being "graphed" here...
It will depend on what population you're representing, but something like "Things" or "Entities" (if you object to calling a cat a thing). If I go around my apartment counting all the
things, I can plot a graph that looks something like this and label the x axis "Things in my apartment." Not a terribly useful exercise, but there's no reason you can't do it.
The x-axis doesn't
need to be ordinal. I can create a bar graph with "Countries" on the x-axis, "Population" on the y, and label each individual bar with a country's name. That's a perfectly good frequency distribution.
It's being asserted by some that a bimodal distribution is
necessarily ordered. That's not strictly true, it's just that if it isn't ordered, it's not really telling you much. The
reason we call them bimodal distributions, despite the fact that the peaks aren't necessarily of the same frequency, is that a bimodal distribution generally reveals the existence of two distinct groups within a population. The peaks will roughly correspond to the modes of these two groups.
In an
unordered categorical set of data, the mode will be whichever value occurs most frequently. If two values occur at the same frequency, you have two modes. If you categorize 100 individuals into "male", "female", and "other", and end up with 49, 49, and 2 members respectively, that's then a bimodal distribution, where the modes are "male" and "female".
Usually a random sample of human beings is going to be roughly bimodal in this sense, even if we treat it as a binary. What does this tell us? Nothing more than that the number of males and females is approximately the same (I think it's something like 51% female, 49% male. The present is female.)