Ensemble-based approaches to RNA secondary structure prediction have become increasingly appreciated in recent years. Here, we utilize sampling and clustering of the Boltzmann ensemble of RNA secondary structures to investigate whether biological sequences exhibit ensemble features that are distinct from their random shuffles. Representative messenger RNAs (mRNAs), structural RNAs, and precursor microRNAs (miRNAs) are analyzed for nine ensemble features. These include structure clustering features, the energy gap between the minimum free energy (MFE) and the ensemble, the numbers of high-frequency base pairs in the ensemble and in clusters, the average base-pair distance between the MFE structure and the ensemble, and between-cluster and within-cluster sums of squares. For each of the features, we observe a lack of significant distinction between mRNAs and their random shuffles. For five features, significant differences are found between structural RNAs and random counterparts. For seven features including the five for structural RNAs, much greater differences are observed between precursor miRNAs and random shuffles. These findings reveal differences in the Boltzmann structure ensemble among different types of functional RNAs. In addition, for two ensemble features, we observe distinctive, non-overlapping distributions for precursor miRNAs and random shuffles. A distributional separation can be particularly useful for the prediction of miRNA genes.