5.1.4—A cumulative frequency graph e

Cumulative frequency totals observations up to each boundary. On a cumulative-frequency graph, read the median at N/2, quartiles at N/4 and 3N/4, and use differences to estimate an interquartile range.

Use class boundaries, draw a smooth monotone curve only as an approximation, and read values against the horizontal axis carefully.

For N=80, the upper quartile is the x-value at cumulative frequency 60; IQR is Q3−Q1.

Cumulative frequency itself is not a percentile value, and a graph gives an estimate rather than an exact raw-data quartile.