       Q on COMBINING PLOTS w/ diff. axes.

• To: mathgroup at smc.vnet.net
• Subject: [mg2377]Q on COMBINING PLOTS w/ diff. axes.
• From: Zorro <berriz at husc.harvard.edu>
• Date: Sun, 29 Oct 1995 22:49:49 -0500
• Organization: Harvard University, Cambridge, Massachusetts

```
I often want to superimpose two graphs that have different vertical or
horizontal axes.  Typically, I want to show how two physical
quantities, with different units, vary as a function of the same
independent variable.  Since the ordinate units are different, I would
like to be able to show two different scales on the ordinate axis.
Less frequently, the plots have the same ordinate units, but differ in
the abscissa variable.

The latter situation happens, for example, when I try to superimpose
experimental frequency histograms produced with the graphics package
function BarChart, onto the graph of the analytical expression for the
corresponding probability density function.  This is because BarChart
uses the bin number as the abscissa variable, regardless of the actual
physical range it represents.  Therefore, as a rule, the histogram
abscissa will conflict with the domain of the probability distribution
function.  For example, say I have an expression for a function
P:[0,1] -> R representing a probability density on the interval [0,1],
and in addition, I have experimental data of frequencies, that I can
convert to a histogram.  If the histogram has, say, 20 bins, then
Mathematica defines the "abscissa range" of the resulting histogram
plot to be something like [1,20], instead of having the same domain as
P, which is, obviously, [0,1].

So my question are 1) in general, how does one get Mathematica to
superimpose plots with different units on the vertical or horizontal
axis, and 2) in particular, how does one get it to display histograms
and functions together?

Any words of wisdom?

Thanks.

Z.

```

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