Worked examples on Ogive

There are two ways of constructing an ogive or cumulative frequency curve. (Ogive is pronounced as O-jive). The curve is usually of 'S' shape. We illustrate both methods by examples given below:

Draw a 'less than' ogive curve for the following data:

To Plot an Ogive:

(i) We plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (10, 2), (20, 10), (30, 22), (40, 40), (50, 68), (60, 90), (70, 96) and (80, 100) are the coordinates of the points.

(ii) Join the points plotted by a smooth curve.

(iii) An Ogive is connected to a point on the X-axis representing the actual lower limit of the first class.

Scale:

X -axis 1 cm = 10 marks, Y -axis 1cm = 10 c.f.

Using the data given below, construct a 'more than' cumulative frequency table and draw the Ogive.

To Plot an Ogive

(i) We plot the points with coordinates having abscissae as actual lower limits and ordinates as the cumulative frequencies,

(70.5, 2), (60.5, 7), (50.5, 13), (40.5, 23), (30.5, 37), (20.5, 49),

(10.5, 57), (0.5, 60) are the coordinates of the points.

(ii) Join the points by a smooth curve.

(iii) An Ogive is connected to a point on the X-axis representing the actual upper limit of the last class [in this case) i.e., point (80.5, 0)].

Scale:

X-axis 1 cm = 10 marks

Y-axis 2 cm = 10 c.f

To reconstruct frequency distribution from cumulative frequency distribution.

When we write, 'less than 10 - less than 0', the difference give the frequency 4 for the class interval (0 - 10) and so on.

When we write 'more than 0 - more than 10', the difference gives the frequency 4 for the class interval (0 - 10) and so on.