Question

For the following distribution draw a ‘less than type’ ogive and from the curve find the median.

Marks obtained	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80	Less than 90	Less than 100
Number of students	2	7	17	40	60	82	85	90	100

Answer 1

1. Identify the coordinates for plotting

To plot a ‘less than type’ ogive, take the upper class limits on the X-axis and their corresponding cumulative frequencies on the Y-axis. The points to be plotted on your graph paper are:

Upper Class Limits (X-axis)	Cumulative Frequency (Y-axis)	Points (x, y)
Less than 20	2	(20, 2)
Less than 30	7	(30, 7)
Less than 40	17	(40, 17)
Less than 50	40	(50, 40)
Less than 60	60	(60, 60)
Less than 70	82	(70, 82)
Less than 80	85	(80, 85)
Less than 90	90	(90, 90)
Less than 100	100	(100, 100)

2. Plot the cumulative frequency curve (Ogive)

1. Choose an appropriate scale on your graph paper (e.g., 1 cm = 10 units on both axes).
2. Plot the coordinate points from the table above and join them using a smooth free-hand curve.

3. Find the median from the curve

1. Compute the middle position of the data, which is given by `N/2`, where N = 100 (total number of students):

`N/2 = 100/2 = 50`

2. Locate the value 50 on the Y-axis (cumulative frequency).

3. Draw a horizontal line from y = 50 parallel to the X-axis until it intersects the curve.

4. From this intersection point, drop a perpendicular line vertically down to the X-axis.

5. The point where this line intersects the X-axis yields the value 55, which is the graphical median.