OGIVE CURVES

   


     OGIVE CURVES

                    Ogive curves are cumulative frequency curves. There are two types of Ogive curves: Less than type and more than type. The construction of these curves is done as below. In the following table class of marks are given with frequency of students in each class.

                   Construction of less than Ogive curve: Start form the upper limit of the first class and write down “less than 10” 20, 30 ------in the column. The point on the graph will be upper limit of the respective class which is shown in a separate column. Now in the next column (5) we need to write number of students obtained less than 10 marks. In our case it is 10. In the next row “less than 20” we have to add number of students in the class 0-10 and 10-20. This process shall be completed till end. It is just cumulative addition of frequencies. Now taking upper limit and cumulative frequency as co-ordinates of X and Y axis draw the graph.

                      Construction of more than Ogive curve: Start form the lower limit of the first class and write down “more than and equal to 0” 10, 20, 30 ------in the column. As lower limit is considered in the class interval we have taken it as ‘more than and equal to’ instead of simply ‘more than’.  The lower limits are written in a separate column (7). Now in the next column (8) we need to write number of students obtained more than or equal to 0 marks. This means all students = 200 Nos. In the next row of column (8) we need to deduct frequency of the previous class. In our case it is 200-2 = 198. This process shall be completed till end. It is just cumulative addition of frequencies from bottom. Now taking lower limit and cumulative frequency as co-ordinates of X and Y axis draw the graph.

Given		Less than Ogive frequency distribution			Less than Ogive frequency distribution
Class of marks	Frequency of students	Less than limit	point on graph	Cumulative frequency ( Less than Ogive)	More than limit	point on graph	Cumulative frequency (More than Ogive)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
0-10	2	Less than 10	10	2	More than or equal to or equal to 0	0	200
.10-20	5	Less than 20	20	7	More than or equal to 10	10	198
20-30	12	Less than 30	30	19	More than or equal to 20	20	193
30-40	21	Less than 40	40	40	More than or equal to 30	30	181
40-50	38	Less than 50	50	78	More than or equal to 40	40	160
50-60	60	Less than 60	60	138	More than or equal to 50	50	122
60-70	33	Less than 70	70	171	More than or equal to 60	60	62
70-80	19	Less than 80	80	190	More than or equal to 70	70	29
80-90	7	Less than 90	90	197	More than or equal to 80	80	10
90-100	3	Less than 100	100	200	More than or equal to 90	90	3
Total	200

Application/ use of Ogive curves: On the basis of graph we can find out Median as it is intersection of the both (less than and more than) curves. Various partition values such as: Q1, Q3 (First and third quartiles), Deciles such as D6, D4 and percentiles such as P5 and P95 can be directly obtained from the less than type Ogive curve. These quartile values are important for construction of Box-plot. We can also find out the percentage of the distribution that falls below or above a given value. How many students got less than 50 marks or 70 marks can be known by using this curve. Similarly answers to the questions how many students obtained more than or equal to 50 marks or 70 marks can be obtained from more than Ogive curve.

A company has 300 employees getting different pay scale depending upon experience, work importance and education. Then the question how many employees are getting payment less than Rs. 12000/- or above 50,000/- can be known using this graph. Similarly the median and quartile values can be defined.

 Dr. Rajeshwar W. Hendre 7709063121, rajeshwar.hendre1966@gmail.com