Graphical Location using the Ogive

Partition values of a continuous distribution can be read straight off an ogive — the graph of the less-than cumulative frequency curve.

Drawing the less-than ogive.

1. Plot the upper boundary of each class along the horizontal ($x$) axis against its less-than cumulative frequency on the vertical ($y$) axis.
2. Begin the curve at the lower boundary of the first class (cumulative frequency $0$) and join the points with a smooth rising curve. The curve ends at the point $(\text{highest boundary},\ N)$.

Reading a partition value off the ogive.

• Mark the locating figure on the $y$-axis — $\tfrac{N}{4}$ for $Q_1$, $\tfrac{N}{2}$ for $Q_2$, $\tfrac{3N}{4}$ for $Q_3$ (or $\tfrac{jN}{10}$, $\tfrac{kN}{100}$ for a decile or percentile).
• Draw a horizontal line from that mark across to the ogive.
• From where it meets the curve, drop a vertical line to the $x$-axis. The foot of that vertical is the required partition value.