This study considers the measurement of Statistical Literacy understanding that goes beyond the basic chance and data skills and knowledge in the mathematics curriculum. This understanding requires application of mathematical skills in a range of contextual situations and draws on aspects of statistics, such as variation and inference, which may not be explicit in the school curriculum. The study reports the outcomes from tests of Statistical Literacy given to 673 students from Grades 5 to 10. It confirms the nature and structure of a previously identified construct of Statistical Literacy and proposes three subgroups of items that address aspects of Statistical Literacy that might usefully be measured by classroom teachers.