Graphical Location of Partition Values Using an Ogive

Just as the median of a continuous series can be read off graphically from the point where the 'less than' and 'more than' ogives intersect, EVERY quartile, decile and percentile can be located graphically from a single 'less than' ogive alone, without drawing the falling ogive at all.

Steps to locate a partition value graphically:

1. Draw the 'less than' ogive: plot cumulative frequency against the UPPER boundary of each class, and join the plotted points with a smooth rising curve.
2. On the Y-axis (cumulative frequency), mark off the required position — $N/4$ for $Q_1$, $3N/4$ for $Q_3$, $iN/10$ for $D_i$, or $iN/100$ for $P_i$.
3. From that point on the Y-axis, draw a line parallel to the X-axis until it meets the ogive.
4. From the point where it meets the curve, drop a perpendicular down to the X-axis. The value read off the X-axis is the required partition value.

<!-- FIGURE-NEEDED: ogive — a 'less than' cumulative-frequency ogive (smooth rising curve) plotted for a continuous wage/marks distribution, with three horizontal guide-lines drawn at cumulative-frequency heights N/4, N/2 and 3N/4, each dropping down via a vertical guide-line to mark Q1, Q2(=Median) and Q3 on the X-axis, illustrating the graphical method of locating quartiles from a single ogive --> …