A frequency curve graphically represents a frequency distribution as a smooth curve. It depicts the limiting case of a histogram as the number of data points becomes very large. An ogive or cumulative frequency curve plots cumulative frequencies on the y-axis against class boundaries on the x-axis. It can show both less than and greater than cumulative frequencies based on a frequency table. The document provides an example of marks data to construct less than and greater than cumulative frequency curves from their respective tables.

1. FREQUENCY CURVE AND OGIVE
REPRESENTING DATA &
INTERPRETATION

2. FREQUENCY CURVE
 A curve that graphically represents a frequency distribution.
OR
 A smooth curve which corresponds to the limiting case of a histogram
computed for a frequency distribution of a continuous distribution as the
number of data points becomes very large.

3. Eg: The following table gives the distribution of the
marks of 100 students in an examination.
Marks Number of students
0-10 5
10-20 10
20-30 18
30-40 26
40-50 22
50-60 15
60-70 4

5. CUMULATIVE FREQUENCY CURVE
OR OGIVES
 The curve obtained by plotting cumulative frequencies.
 An ogive graph plots cumulative frequency on the y-axis and class boundaries
along the x-axis.

6. Eg:- Draw the less than and greater than cumulative
frequency curve from the following frequency table.
Class interval Frequency
0-20 3
20-40 10
40-60 15
60-80 18
80-100 8
100-120 6

7. LESS THAN CUMULATIVE FREQUENCY TABLE
Upper bound Less than cumulative frequency
20 3
40 13
60 28
80 46
100 54
120 60

8. LESS THAN CUMULATIVE FREQUENCY CURVE

9. GREATER THAN CUMULATIVE FREQUENCY TABLE
Lower bound Greater than cumulative frequency
0 60
20 57
40 47
60 32
80 14
100 6

10. GREATER THAN CUMULATIVE FREQUENCY CURVE

11. LESS THAN & GREATER THAN CUMULATIVE
FREQUENCY CURVE

12. Thank you