CUMULATIVE FREQUENCY POLYGON or OGIVE
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The document defines a cumulative frequency polygon (or ogive) as a graph of a cumulative frequency distribution where the upper class boundaries of a data set are plotted along the x-axis and the cumulative frequencies are plotted along the y-axis. An example is provided of age data for 50 childcare managers categorized into classes, with the corresponding frequency distribution and cumulative frequency distribution calculated and plotted on a cumulative frequency polygon.
CUMULATIVE FREQUENCY POLYGON or OGIVE
- 1. The graph of a cumulative frequency distribution is called a CUMULATIVE FREQUENCY POLYGON or OGIVE. A ogive is obtained by marking off the upper class boundaries of the various classes along the X-axis and the cumulative frequencies along the y-axis, as shown below: CUMULATIVE FREQUENCY POLYGON or OGIVE
- 2. Example The following table contains the ages of 50 managers of child-care centers in five cities of a developed country. Construct the cumulative frequency distribution and the cumulative frequency polygon (ogive).
- 3. Ages of a sample of managers of Urban child-care centers 42 26 32 34 57 30 58 37 50 30 53 40 30 47 49 50 40 32 31 40 52 28 23 35 25 30 36 32 26 50 55 30 58 64 52 49 33 43 46 32 61 31 30 40 60 74 37 29 43 54 Convert this data into Frequency Distribution.
- 4. Frequency Distribution of Child-Care Managers Age Class Limits Frequency 20 – 29 6 30 – 39 18 40 – 49 11 50 – 59 11 60 – 69 3 70 – 79 1 Total 50
- 5. Cumulative Frequency The cumulative frequency is the running total of the frequencies through the total. The cumulative frequency for each class interval is the frequency for that class interval added to the preceding cumulative total.
- 6. Cumulative frequencies of child- care data Class Limits Frequency Cumulative frequency 20 – 29 6 6 30 – 39 18 24 40 – 49 11 35 50 – 59 11 46 60 – 69 3 49 70 – 79 1 50 Total 50
- 7. Interpretation 24 of the 50 managers (i.e. 48% of the managers) are 39 years of age or less. (i.e. less than 40 years old.) 46 of 50 managers (i.e. 92% of the managers) are 59 years of age or less. (i.e. less than 60 years old.) and so on.
- 8. Cumulative frequency polygon or Ogive 0 10 20 30 40 50 60 19.5 29.5 39.5 49.5 59.5 69.5 79.5
- 9. Example Suppose we walk in the nursery class of a school and we count the no. of Books and copies that 45 students have in their bags. Suppose the no. of books and copies are 9,9,3,5,4,7,6,7,5,6,5,5,8,7,5,5,6,6,6,9,6, 7,6,6,4,5,5,6, 6,6,6,7, 7,8, 5,8,8, 7, 9, 9,7, 8,7,7,9,.
- 10. Representation of Data in a Discrete Frequency Distribution X Tally Frequency 3 | 1 4 ||| 3 5 |||| |||| 9 6 |||| |||| ||| 13 7 |||| |||| 10 8 ||| 3 9 |||| | 6 Total 45
- 11. Graphical Representation of Discrete Data 8 10 12 2 4 6 0 X 14 No. of books and copies No.ofstudents
- 12. Relative Frequency Distribution X Frequency Relative/ % Frequency 3 1 1/45 x 100 = 2.22% 4 3 3/45 x 100 = 6.67% 5 9 9/45 x 100 = 20% 6 13 13/45 x 100 = 28.89% 7 10 10/45 x 100 = 22.22% 8 3 3/45 x 100 = 6.67% 9 6 6/45 x 100 = 13.33% Total 45
- 13. Cumulative Frequency Distribution X Frequency Cumulative Frequency 3 1 1 4 3 1+3 = 4 5 9 4+9 = 13 6 13 13+13 = 26 7 10 26+10 = 36 8 3 36+3 = 39 9 6 39+6 = 45 Total 45
Editor's Notes
- #9: WE TAKE UPPER CLASS BOUNDARIES OF ALL THE CLASSES ALONG X AXIS BUT WE ALSO TAKE LOWER CLASS BOUNDARY OF FRST CLASS AND CONSIDER ITS FREQUENCY ZERO TO CLOSS THE CUTVE TOMAKE A POLYGON.