128 – Curricular Considerations for Statistics and Data Science Education
Statistical Literacy and the Lognormal Distribution
Milo Schield
Augsburg University
Income inequality is a hot topic. There is no public data on the income share of the top 1% of households; those percentages are estimates. Those estimates vary from 5% to 40%. They are based on different data using different definitions and different models. This paper studies a common model: the log-normal distribution. This paper shows six things for any log-normal distribution. (1) The mean-median ratio determines the shape of the distribution, the income share of the top 1%, and the Gini coefficient. (2) The log-normal model is a fairly good fit to the actual distribution of 2016 US household incomes. (3) If the distribution of subjects by income is log-normal, then the distribution of total income by household income will also be log-normal. (4) The percentage of subjects that have below-average incomes always equals the percentage of total income that is earned by those with above-average income. (5) These below/above percentages can be used to measure income inequality in a way that is more accessible than the Gini coefficient. (6) The product of a normal and a log-normal can be modeled as the product of two log-normal distributions. Including the log-normal distribution in a statistical literacy class helps decision makers focus on essentials.