Cumulative frequency

A cumulative frequency graph answers a different question: how many observations are at or below a value? Start with the first class frequency and keep adding. Plot each running total against the upper boundary of its class, not its midpoint.

Histograms and cumulative frequency graphs are particularly useful for grouped numerical data. A histogram shows how observations are distributed across the intervals. A cumulative frequency graph instead shows how many observations lie below successive class boundaries, so it is useful for estimating medians, quartiles, percentiles and the number below or above a chosen value.

Histograms reveal how observations are distributed among the intervals, while cumulative frequency graphs reveal how their running total builds up.