Say I have a bar graph with one dependent variable and one independent variable. Given a time $t$, I essentially want to modify the given graph so that as $t -> \infty$, all the bars become equal to the mean.
In other words, I essentially want to move the bars of the graph, so that the bars above the mean lower so that they are closer to it and bars below it rise so that they are also closer to it.
I would like to the transformation to happen in negative exponential time (In other words, the bars move a lot initially, and they only converge to the mean when after an infinite amount of time)
At any time, the mean value of the graph must be equal to the original mean.
Any ideas how I can do this? I've never really worked with statistics before.
Figured it out:
The $y$ value of value $x$ at a time $t$ is $x_i + (m - x_i)e^{-t}$
where $x_i$ is the value at time 0 and $m$ is the original mean.