Graphic location of Median

Median and other partition values can be located on 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:


graphic-location-median

For median, we calculate n/2. On the Y-axis we mark the height equal to n/2 and from this point we draw a straight line parallel to the X-axis which intersects the polygon at point m. From point m we draw a perpendicular which touches the X-axis at M. This point on the X-axis is the median. Similarly, for the lower quartile we take a height equal to n/4 on the Y-axis. From this we draw a line parallel to the X-axis which intersects the polygon at point q. From this point we draw a perpendicular on the X-axis which touches it at point Q1, which is the first quartile. For the upper quartile take the height on the Y-axis equal to3n/4.