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How to Graph an Ogive

Ogive Graph Definition:
A graph of frequency distribution which summarize the percentage of data either lower level or higher level related to the given data.When the data are plotted in the graph an S-shaped curve similar to a part of the parabola is formed which shows increasing numbers or percentage that eventually reaches 100%.The general Histogram and Ogive graph varies in shapes and depending on the frequency. For given cumulative frequency Ogive graph increases from 0% to 100%.

Cumulative Frequency:
A frequency distribution indicates the number of individual events occurred. A cumulative frequency indicates the successive addition of a number of events occurred  in the given categories, which adds up to the value of 100.

Types of Ogive: 
There are two types of Ogive graph lower than Ogive and Greater than Ogive.
  1. Lower than Ogive: The cumulative frequency are arranged in ascending order and plotted against upper class level.
  2. Greater than Ogive: The cumulative frequency are arranged in descending order and plotted against lower class level.

How to Make Ogive Graph:

To make an Ogive graph we need to work out with cumulative frequency, each frequency is added with next frequency. The following steps are taken to draw an Ogive graph.

              Step 1: Frequencies are added to get cumulative frequencies.
              Step 2: Write down only the class interval with an upper limit of each class and cumulative relative frequency in another                                 tabular column.
              Step 3: Plot the order pair on a graph in ordered pair with respect upper limit of each class and cumulative frequencies.

Example Problems:

   1. Consider the following distribution and plot the Ogive graph             
                                  
          Class                  1-10        11-20       21-30       31-40      41-50       51-60   
 Frequency   18  14  13  10  8  6

Solution: Use the above table to draw Ogive graph

Step 1: Frequencies are added to get cumulative frequencies.

       Class            Frequency         Cumulative Frequency      
 1-3  2.5  2.5
 3-5  7.5  10
 5-7  10  20
 7-9  12.5  32.5
 9-11  25  57.5
 11-13  22.5  80
 13-15  7.5  87.5

Step 2: 

         Class               Cumulative Frequency       
 3  2.5
 5  10
 7  20
 9  32.5
 11  57.5
 13  80
 15  87.5


Ogive Graph