Generating distribution of data with known mean, median, range, and total data ponts

Question

Is there a formula to create either data in cells or plot a graph to determine generally where the data points are? I have the following to reference:
Mean = 190
Median = 69
Min=0
Max=36046
Total data points=115417

I didn't take a Stats class in school and it shows, but I know that there is such an extreme positive skew because there most likely ALOT of data points equal to or near 0. So my goal is to try and find that number, percentage or likelihood if possible.

Apologies for the ignorant Q but thank you to anyone who can lend some guidance.

Answer 1

Unfortunately, there's lots of distributions that could produce those statistics.

To see that, imagine you have a distribution that produces those statistics. Take a point that is between $0$ and the median. Call that point $a$. Take another point that is above the median but sufficiently away from the max. Call that point $b$. If we change $b$ to be $a+b$ and change $a$ to be $0$, then our mean, median, min, max, and total data points will all be the same, but we increased our number of $0$s by $1$. And we can do this over and over again to change our number of $0$s while keeping those same statistics. So, without more information, you can't really determine the number of $0$s.