# Graphic Location of Median

Median and other partition values can be located from the graph of the cumulative frequency polygon (Ogive Polygon). Suppose we have a graph of the cumulative frequency polygon as shown in the figure below.

For median, we calculate $n/2$. On Y-axis, we mark the height equal to $n/2$ and from this point we draw a straight line parallel to X-axis which intersects the polygon at the point m. from the point m, we draw a perpendicular which touches the X-axis at M. This point on X-axis is the median. Similarly, for the lower quartile we take height equal to $n/4$ on the Y-axis. From this we draw a line parallel to X-axis which the polygon at the point q. From this point we draw perpendicular on X-axis which touches it at the point Q1 which is the first quartile. For upper quartile take the height on Y-axis equal to$3n/4$.