EDU.08
Assessment in Education
Seminar
Topic- Ogives
Submitted by
Anju J
Submitted to
Miss PARVATHY V PRASAD
Ogives or cumulative frequency curve
We have seen that there are two types of cumulative frequency tables
1. Less than cumulative frequency table
2. Greater than cumulative frequency table.
The curve drawn by plotting points with the upper bounds of classes as. X_ coordinates and the corresponding less than cumulative frequencies as Y_ coordinates and joining these points by a smooth curve starting from the lower bound of the first class is called a less than ogive.
Similarly by plotting points with the lower bounds of classes as X coordinates and the
corresponding greater than cumulative frequencies as the Y coordinates and joining them by a smooth curve which meets the Z-axis at the upper bound of the last class is called ogive.
We may also draw a step diagram or a cumulative polygon for a cumulative frequency distribution. If horizontal lines are drawn over each class at a height equal to the cumulated frequencies and the end points of successive horizontal lines joined by vertical lines we get a step diagram. We can have less than as well as greater than step diagrams. If the points with class boundaries and the corresponding cumulative frequencies as coordinates are joined by straight lines successively,we get a cumulative polygon. But cumulative frequency curves and particularly less than cumulative frequency curves are most important.
Example 1
The following table gives the distribution of the marks of 100 students in an
Examination. Draw the two Ogives of the frequency distribution.
Marks 0-10 10-20 20-30 30-40
No.if students. 5 10 18 26
40-50 50-60 60-70
22 15 4
Answer
First the less than and greater than cumulative frequency tables are to be prepared.
Less than cumulative frequency table
Upper bounds less than
Of classes cumulative frequency
10 5
20 15
30 33
40 59
50 81
60 96
70 100
Greater than cumulative frequency table
Lower bounds greater than
Of classes cumulative frequency
0 100
10 95
20 85
30 67
40 41
50 19
60 4
Example 2
Draw the ogive for the following data
Mid x 5 10 15 20 25 30
frequency 10 12 85 100 80 13
when it is not specified whether less than ogive or greater than ogive is to be drawn it is conventional to drawn the less than ogive. here only the mid values of the classes are given. so we have to find out the upper bounds of the classes. the upper bound of the first class is (5+10)/2=7.5 and the class interval is 5. so the upper bound of the classes are 7.5 , 12.5,17.5,22.5,27.5,32.5. now the less than cumulative frequency table may be prepared . the ogive is given in figure.
upper bound of the classes less than cumulative frequency
7.5 10
12.5 22
17.5 107
22.5 207
27.5 287
32.5 300
Assessment in Education
Seminar
Topic- Ogives
Submitted by
Anju J
Submitted to
Miss PARVATHY V PRASAD
Ogives or cumulative frequency curve
We have seen that there are two types of cumulative frequency tables
1. Less than cumulative frequency table
2. Greater than cumulative frequency table.
The curve drawn by plotting points with the upper bounds of classes as. X_ coordinates and the corresponding less than cumulative frequencies as Y_ coordinates and joining these points by a smooth curve starting from the lower bound of the first class is called a less than ogive.
Similarly by plotting points with the lower bounds of classes as X coordinates and the
corresponding greater than cumulative frequencies as the Y coordinates and joining them by a smooth curve which meets the Z-axis at the upper bound of the last class is called ogive.
We may also draw a step diagram or a cumulative polygon for a cumulative frequency distribution. If horizontal lines are drawn over each class at a height equal to the cumulated frequencies and the end points of successive horizontal lines joined by vertical lines we get a step diagram. We can have less than as well as greater than step diagrams. If the points with class boundaries and the corresponding cumulative frequencies as coordinates are joined by straight lines successively,we get a cumulative polygon. But cumulative frequency curves and particularly less than cumulative frequency curves are most important.
Example 1
The following table gives the distribution of the marks of 100 students in an
Examination. Draw the two Ogives of the frequency distribution.
Marks 0-10 10-20 20-30 30-40
No.if students. 5 10 18 26
40-50 50-60 60-70
22 15 4
Answer
First the less than and greater than cumulative frequency tables are to be prepared.
Less than cumulative frequency table
Upper bounds less than
Of classes cumulative frequency
10 5
20 15
30 33
40 59
50 81
60 96
70 100
Greater than cumulative frequency table
Lower bounds greater than
Of classes cumulative frequency
0 100
10 95
20 85
30 67
40 41
50 19
60 4
Example 2
Draw the ogive for the following data
Mid x 5 10 15 20 25 30
frequency 10 12 85 100 80 13
when it is not specified whether less than ogive or greater than ogive is to be drawn it is conventional to drawn the less than ogive. here only the mid values of the classes are given. so we have to find out the upper bounds of the classes. the upper bound of the first class is (5+10)/2=7.5 and the class interval is 5. so the upper bound of the classes are 7.5 , 12.5,17.5,22.5,27.5,32.5. now the less than cumulative frequency table may be prepared . the ogive is given in figure.
upper bound of the classes less than cumulative frequency
7.5 10
12.5 22
17.5 107
22.5 207
27.5 287
32.5 300
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