What are ogives? Discuss the method of constructing ogives with the help of an example

by

An ogive, also known as a cumulative frequency curve, is a graphical representation of cumulative frequency distribution.

It displays the cumulative frequency of a dataset at or below certain values. Ogives are useful for visualizing the distribution of data and identifying patterns in the cumulative frequencies.

Here’s a step-by-step method for constructing an ogive:

Method of Constructing Ogives:

  1. Prepare the Frequency Distribution Table:
  • Begin with a frequency distribution table that includes columns for the data intervals (classes), frequencies, and cumulative frequencies. Class Interval Frequency (f) Cumulative Frequency (CF) 0-10 5 10-20 8 20-30 12 30-40 7 40-50 10
  1. Calculate Cumulative Frequencies (CF):
  • Determine the cumulative frequency for each class interval by adding the frequency of that interval to the cumulative frequency of the previous interval.
  • For the given example:
    • ( CF_{10} = 5 )
    • ( CF_{20} = CF_{10} + 8 = 13 )
    • ( CF_{30} = CF_{20} + 12 = 25 )
    • ( CF_{40} = CF_{30} + 7 = 32 )
    • ( CF_{50} = CF_{40} + 10 = 42 )
  1. Plotting the Ogive:
  • Use a graph paper and draw a set of axes. The x-axis represents the data intervals, and the y-axis represents cumulative frequencies.
  • Mark the lower class boundaries (midpoints) on the x-axis and the corresponding cumulative frequencies on the y-axis.
  1. Drawing the Ogive:
  • Starting from the first point (0, 0), plot the points for each class interval using the lower class boundaries and the corresponding cumulative frequencies.
  • Connect the points using straight lines to form the ogive.

Example:

Suppose you have the following frequency distribution table for exam scores:

Class Interval   Frequency
0-10              5
10-20             8
20-30             12
30-40             7
40-50             10

Now, let’s construct the ogive:

  1. Calculate Cumulative Frequencies:
   CF_10 = 5
   CF_20 = CF_10 + 8 = 13
   CF_30 = CF_20 + 12 = 25
   CF_40 = CF_30 + 7 = 32
   CF_50 = CF_40 + 10 = 42
  1. Plotting the Ogive:
   Data Intervals   Cumulative Frequencies
   0-10             | 5
   10-20            | 13
   20-30            | 25
   30-40            | 32
   40-50            | 42
  1. Drawing the Ogive:
  • Plot the points (10, 5), (20, 13), (30, 25), (40, 32), and (50, 42).
  • Connect the points with straight lines to form the ogive.

The resulting graph will display the cumulative distribution of exam scores, providing insights into the overall performance of the dataset.