Understanding what is communicated by data visualizations is a critical component of scientific literacy in the modern era. However, it remains unclear why some tasks involving data visualizations are more difficult than others. Here we administered a composite test composed of five widely used tests of data visualization literacy to a large sample of U.S. adults (N=503 participants). We found that items in the composite test spanned the full range of possible difficulty levels, and that our estimates of item-level difficulty were highly reliable. However, the type of data visualization shown and the type of task involved only explained a modest amount of variation in performance across items, relative to the reliability of the estimates we obtained. These results highlight the need for finer-grained ways of characterizing these items that predict the reliable variation in difficulty measured in this study, and that generalize to other tests of data visualization understanding.