Which statistical test to use for multi-modal and mixed type data?

tintin84hh

New Member
I researched for hours but cannot find the direction for the right statistical test to use. Here is the situation for Population A and B:

When plotting this frequency distribution, it looks like this:

My observations to this point:
- Shape: Multi-modal
- Data type: Discrete

- Typically amounts are discrete such as: $1,$5, $10,$20 dollars
-The mean of A: $7.11 and B:$7.49
-The standard deviation of both is the same $8.00 The goal is to compare if the means of the two populations (A and B) differ. This means we need the right statistical test and that is the issue I have. I researched days and cannot find a solution which includes the complexities in my situation. What is the right test for this? Also, is it recommended to re-arrange the bins where exact amounts ($5,$10,$20) are put in bins with a range to avoid the mix of bins with range and bins without range?