Build and verify frequency distributions

An ungrouped table lists values and counts f. A grouped table combines values into nonoverlapping classes covering the observations. The total N = ∑f must match the number of observations. Relative frequency is f/N, or 100f/N percent. Cumulative frequency is a running total. A class midpoint is the average of its limits. For values rounded to whole units, class 20-29 has boundaries 19.5 and 29.5 and width 10.