Histogram graph given variance and mean value

Question

Is it possible to construct the histogram graph given the variance and the mean value of the samples?

Answer 1

You can only do that for very specific theoretical distributions such as the Normal distribution (and then again, you would represent a density function rather than a real histogram).

For regular data, two numbers are not enough to represent hundreds or thousands of values.

Answer 2

No. Consider $\{0\}$ and $\{0,0\}$. Both have mean and variance $0$ but different histograms.