For example, given the data set:

category A: 11

category B: 13

category C: 15

category D: 22

category E: 33

category F: 15

category G: 5

I know that there are 114 items in the population, a skewness of 1.05 and a kurtosis of 1.56.

Is there any way to reverse this and get an approximation of the values? If I know the population size of 114 and the skewness and kurtosis values, can I somehow approximate the values in each category?