How to sample a statistically uniform dataset
There are a variety of sampling options:


Sample directly from the data which perfectly models the empirical distribution. 
Fit a kernel density estimation (kde). Sample from the estimated kde function.
Create a histogram of the data, aka bin the data. Then treat each histogram as a probability mass function (pmf). Sample from bins proportional to their frequency.


You can create variations of the data or distributions:


Apply a transformation to the data. For example, a log transformation will transform skewed distribution to be more normal.
The histogram values could be changed to any shape.


Then sample from the changed data or distributions.

The most extreme option would define a uniform distribution across the data domain and sample from that distribution. The green box is a uniform distribution.