Less than Ogive

The steps required to present a less than ogive graph are as follows:

Step 1: To present a less than ogive graph, add the frequencies of all the preceding class intervals to the frequency of a class.

Step 2: After that, plot the less than cumulative frequencies on the Y-axis against the upper limit of the corresponding class interval on the X-axis. 

Step 3: In the last step, join these points by a smooth freehand curve, which is the resulting less than ogive. 

A less than ogive curve is an increasing curve that slopes upwards from left to right. 

Example:

Draw a ‘less than’ ogive curve from the following distribution of the marks of 50 students in a class. 

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of Students	6	4	15	5	8	7	5

Solution:

First of all, we have to convert the frequency distribution into a less than cumulative frequency distribution. 

Marks	No. of Students (f)	No. of Students (cf)
Less than 20	6	6
Less than 30	4	6 + 4 = 10
Less than 40	15	6 + 4 + 15 = 25
Less than 50	5	6 + 4+ 15 + 5 = 30
Less than 60	8	6 + 4 + 15 + 5 + 8 = 38
Less than 70	7	6 + 4 + 15 + 5 + 8 + 7 = 45
Less than 80	5	6 + 4 + 15 + 5 + 8 + 7 + 5 = 50

Now, plot these values of cumulative frequency on a graph. 

A method of presenting data in the form of graphs that provides a quick and easier way to understand the trends of the given set of data is known as Graphic Presentation. The two types of graphs through which a given set of data can be presented are Frequency Distribution Graphs and Time Series Graphs. The four most common graphs under Frequency Distribution Graphs are Line Frequency Graph, Histogram, Frequency Polygon, Frequency Curve, and Ogive.