Statistics-Ogive Graph

In statistics, the frequency distribution is one of the most common tools for organizing data. It is used to group data into categories and show the number of observations in each category using tallies or tally marks. The total frequency of all the classes less than the upper class boundary of a given class is called the cumulative frequency; it is also referred to as the running total of frequencies. When we plot a graph with these cumulative frequencies on the y-axis and the class on the x-axis we get a curve called the cumulative frequency curve, which is also called the Ogive.

Ogive definition: We Define Ogive as a distribution curve in which the frequencies are cumulative.
 An Ogive chart or the cumulative frequency distribution chart consists of mainly three columns, first-displaying the class interval (grouped data) or the class(un-grouped data), second-displaying the frequencies in that class and third- the cumulative frequency of that class. Let us consider an example to understand an Ogive chart better.

Ogive Example: The following table gives the frequency distribution of marks obtained by 25 students in a particular test. Let us construct a cumulative frequency table or the Ogive chart for the given data and then learn to graph it.

Now that we got the cumulative frequencies of each class, we can plot the graph. The cumulative frequency graph or Ogive graph is obtained by plotting the cumulative frequency on the y-axis against the data which is on the x-axis for an un-grouped data. The above given data is an un-grouped data and hence we take, marks on the x-axis and the cumulative frequency on the y-axis. Once the points are plotted, we join them to get a curve. The curve thus obtained is the Ogive graph or the cumulative frequency curve.

Ogive Example: In a chess tournament, there were 10 participants who had to fill the entry forms that gave their personal details, name, address and age.  The following are the ages recorded. Plot a cumulative frequency graph (Ogive) for the given data:  48, 37, 63, 66, 78, 90, 56, 46, 84, 62
Solution: The given data is a grouped data. So we need to divide the results into intervals and then tabulate the data. The lowest age being 37, let us consider the lower value to be 35 and class interval as 10
37, 46, 48,56, 62, 63, 66, 78, 84, 90

We now plot the graph using the cumulative frequency on the y -axis and the upper value on the x-axis. Joining the points we get the Ogive graph (cumulative frequency curve)