When I was in college, I had a proposal for a senior honors thesis in my major (mathematics) regarding issues relevant to a wide variety of social science issues, regarding what the expected amount of inequality in a data set is when the data set is comprised of points like individual income that have a normal distribution, and one multiplies the income amount by the probability of having that income to get a baseline expected level if inequality to which actual data can be compared.
Rather than doing this, social scientists usually use tools like the GINI index that measures inequality in a scale that uses only the extremes of perfect equality and perfect inequality (everything is concentrated in one person) reference points without any acknowledgement that these are wildly unrealistic assumptions and that it is possible to look at what would be expected with more realistic assumptions like a normal distribution of income.
My proposal was denied, in part, I think, because I don't think I conveyed its value and intellectual depth to my adviser. (Honestly, this is probably one of the two or three most disappointing moments in my entire higher educational career, looking back on it.) But, if I had, I would have soon discovered that this was deeply related to the mathematics of lognormal distributions.
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