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This paper explores the quantitative relationships between average levels of learning achievement across countries, changes in average levels of learning achievement, the inequality of distribution of achievement (akin to income or wealth inequality in general development analysis), and the proportion of students learning at or below an absolute minimum (akin to poverty in general development analysis). The paper uses a variety of data from cross-national and national assessments: aggregate data, micro (student-level) data, school-level data, and time-series data. The paper shows how various factors such as gender or wealth impact learning levels, but also shows that ‘systems-related’ inequality, not directly related to such factors, is typically much larger than inequality associated with any of those factors. The paper shows that countries progress from very low average levels of achievement to middle levels more by reducing the percentage of students with very low scores (that is, by paying attention to the ‘bulging’ left-hand tail of the distribution) than by increasing the percentage of high performing students. The availability of micro data from a particular case allows exploration of the relationship between inequality measures and measures of the percentage of students below a low level of achievement and shows that, at least in that case, the reduction in inequality that accompanies improvements in the average levels takes place mostly through a reduction in the percentage below a low level. Unlike in the case of income, where vast reductions in income poverty seem possible without reducing income inequality, the evidence presented here suggests that this typically does not happen with learning levels: inequality reduction, reductions in percentages below a low level, and improvements in the averages are all empirically connected. More work is needed to show whether that connection is also causal.