The curve obtained by freehand drawing of the upper or lower limit of the class interval on the X-axis and the cumulative frequency of the class interval on the Y-axis is called the cumulative frequency curve or ogive.
The freehand drawing of the curved line by marking the points of upper limit of the class interval on the X-axis and the cumulative frequency of the class interval on the Y-axis is called less than cumulative frequency curve or ogive.
Steps of constructing less than cumulative frequency curve or ogive
•Draw X- and Y- axis in the graph paper.
•Mark on X-axis in a suitable scale of upper limit of each class.
•Label the corresponding frequency in Y-axis with a suitable measurement.
•Now, locate the points that intersect the upper limit value of the class and the corresponding frequency in the graph.
•Then, join the points respectively, you can get the less than frequency curve.
Note: Constructing Less Than Cumulative Frequencies
For each class: less than cumulative frequency = sum of frequencies of all classes up to current class.
Example: If total N = 35, less than cumulative frequency for class 20-30 is the sum of frequencies of classes with upper limit up to 30.
Definition & Construction
More Than Cumulative Frequency Curve (Ogive)
Definition
The freehand drawing of the curved line by marking the points of lower limit of the class interval on the X-axis and the cumulative frequency of the class interval on the Y-axis is called more than cumulative frequency curve or ogive.
It is also known as the "greater than ogive". The cumulative frequencies are obtained by successively adding the frequencies starting from the highest class interval down to the lowest class.
Steps of constructing more than cumulative frequency curve or ogive
•Draw X- and Y- axis in the graph paper.
•Mark on X-axis in a suitable scale of lower limit of each class.
•Label the corresponding more than cumulative frequency on Y-axis with a suitable measurement.
•Now, locate the points that intersect the lower limit value of the class and the corresponding more than cumulative frequency in the graph.
•Then, join the points respectively, you can get the more than cumulative frequency curve (ogive).
Note: Constructing More Than Cumulative Frequencies
For each class: more than cumulative frequency = total frequency minus cumulative frequency up to previous class.
Example: If total N = 35, more than freq for class 20-30 is sum of frequencies of classes greater than or equal to 20.