Cumulative Frequency and Percentiles

Cumulative frequency counts observations below a boundary. Plot the lower starting boundary with cumulative frequency zero, then plot each upper class boundary with its running total. Read horizontally from the desired cumulative frequency and vertically down to the data axis. **Summary for twenty observations** | **Cumulative frequency** Lower quartile | 5 Median | 10 Upper quartile | 15 90th percentile | 18 Read the lower and upper quartiles from cumulative frequencies 5 and 15, then subtract to estimate IQR=Q_3-Q_1 in minutes. A reading between class boundaries is an estimate, not an exact observation. The number above a threshold is total frequency minus cumulative frequency at that threshold.