Let us suppose that some real-world experiment is described by a random variable $X$ which is assumed to be (absolutely) continous. The results of the experiment have been written down. My question is how does one recover the density function $f(x)$ such that $P(X\in E) = \int_E f(x)$?
The first idea that I had is to create a histogram plot with a very fine interval subdivision. However, this is not a true histogram plot, rather the height of each bar is replaced by its frequency percentage. We can then connect the midpoints on each bar and get a piecewise linear curve that will approximate some density curve.
However, there is an issue that bothers me. Density functions are not required to satisfy the condition that $0\leq f(x)\leq 1$, while the frequency-percentage histogram plot will generate a function that is bounded in such a way.