Ogive (cumulative relative frequency graph)

An ogive plots the running proportion of the data against the class boundaries: above the top of each class sits the share of all observations at or below it. Because a running total can only grow, an ogive never decreases. It starts at 0 at the bottom boundary and finishes at exactly 1 at the top, and the height at any plotted point answers "what fraction is at or below here".

Take 50 commute times grouped into 10-minute classes, with 6, 15, 17, 8 and 4 commutes in them. The running counts are 6, 21, 38, 46 and 50, so dividing by 50 puts the curve through $(10, 0.12)$, $(20, 0.42)$, $(30, 0.76)$, $(40, 0.92)$ and $(50, 1.00)$.

The misreading to name is this one: "the curve is at 0.76 above 30 minutes, so 76 percent of commutes took between 20 and 30 minutes." The height is cumulative. It counts all 38 commutes of 30 minutes or less, not just the ones in the last class. The share inside the 20 to 30 class is a difference of heights, $0.76 - 0.42 = 0.34$, which is 17 commutes. On an ogive, "at or below" questions are one reading and "inside this class" questions are always a subtraction.

Anything read between two plotted points is an estimate, because grouping threw away the individual values inside each class. The curve crosses 0.500 between $(20, 0.42)$ and $(30, 0.76)$, and straight-line interpolation puts the median near $20 + \frac{0.50 - 0.42}{0.76 - 0.42} \times 10 = 22.35$ minutes. That is an estimate from grouped data, not the median of the raw 50 values. A flat stretch means an empty class, not a gap in the record.

The Fall 2026 AP Statistics course framework does not name the ogive or the cumulative relative frequency graph among its representations, so you are unlikely to be asked to build one, though reading one you are handed is fair game.