13.5 Graphical Representation: The Ogive

1. Prepare Coordinates: We need (Upper Limit, Cumulative Frequency).

• Upper Limit 10: cf = 22 -> Point (10, 22)
• Upper Limit 20: cf = 22+10=32 -> Point (20, 32)
• Upper Limit 30: cf = 32+8=40 -> Point (30, 40)
• Upper Limit 40: cf = 40+15=55 -> Point (40, 55)
• Upper Limit 50: cf = 55+5=60 -> Point (50, 60)

2. Plotting: Plot these points on a graph paper with Rainfall on X-axis and Cumulative Days on Y-axis. Join them with a smooth freehand curve.

3. Finding Median: Total $N = 60$. So $N/2 = 30$. Locate 30 on the Y-axis. Draw a horizontal line to meet the curve. Drop a perpendicular to the X-axis. Reading the graph, the X-value is approx 18.

Calculation Check: Median Class 10-20. $l=10, cf=22, f=10, h=10$. Wait, Median class logic check: $N/2=30$. cf for 0-10 is 22. Next cf is 32. So 30 is in 10-20 class. Correct. Formula: $10 + ((30-22)/10)*10 = 10 + 8 = 18$.