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Measures of Central Tendency MODE (Grouped Data)

Measures of Central Tendency MODE (Grouped Data). Prepared by: Ryan L. Race Jenelyn A. Samsaman Rafaela M. Sarmiento Jorge O. Dela Cruz Maria Theresa S. Parajas Luningning B. Federizo. Purpose/Rationale of this Module.

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Measures of Central Tendency MODE (Grouped Data)

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  1. Measures of Central TendencyMODE (Grouped Data) Prepared by: Ryan L. Race Jenelyn A. Samsaman Rafaela M. Sarmiento Jorge O. Dela Cruz Maria Theresa S. Parajas Luningning B. Federizo

  2. Purpose/Rationale of this Module This module is designed to provide students with a step by step discussion on the computation of the mode for grouped data. It is to let the students discover for themselves how to compute for the mode (grouped data) through an easy visual presentation of the subject. Enjoy!

  3. What Will You Learn From This Module? After studying this module, you should be able to: • Compute the mode for grouped data. • Use mode for grouped data to analyze and interpret data to solve problems in daily life.

  4. Let’s See What You Already Know • Before you start studying this module, take the following test first to find out how prepared you are to solve for the mode of grouped data.

  5. Find the mode of each of the following sets of numbers. a. 2, 4, 5, 1, 4, 6 b. 77, 80, 90, 65, 77, 89, 80 c. 1299, 2580, 4098, 9100, 1100 Answer Answer Answer

  6. Answer: 4 Click me to answer letter b.

  7. Answer: 77 and 80 Click me to answer letter c.

  8. Answer: No Mode Go Back CONTINUE

  9. For the next set of questions, refer to the given frequency distribution table of the grades of a group of students. CONTINUE

  10. 1. What is the modal class? ANSWER

  11. ANSWER: 75 – 79 The modal class is the class with the highest frequency. CONTINUE

  12. 2. What is the lower class boundary of the modal class? ANSWER

  13. ANSWER: Lmo = 74.5 CONTINUE

  14. 3. What is the frequency of the modal class? ANSWER

  15. ANSWER: fmo = 12 CONTINUE

  16. 4. What is the frequency of the class preceding the modal class? ANSWER

  17. ANSWER: f1 = 8 CONTINUE

  18. 5. What is the frequency of the class after the modal class? ANSWER

  19. ANSWER: f2 = 3 CONTINUE

  20. 6. What is the class size? ANSWER

  21. ANSWER: i = 5 CONTINUE

  22. Observe how the modal grade of the students is computed. Mode (Mo) = +{[( – )]/[2( ) – – ]} = 74.5 + (4/13)5 = 74.5 + (20/13) = 76.04 74.5 12 8 12 8 3 5 CONTINUE

  23. 74.5 is the lower class boundary of the modal class (Lmo)

  24. 12 is the frequency of the modal class (fmo)

  25. 8 is the frequency of the class preceding the modal class (f1)

  26. 3 is the frequency of the class after the modal class (f2).

  27. 5 is the class size (i).

  28. How did we solve for the modal grade of the students?Can you give the formula for the mode of grouped data? CONTINUE

  29. To solve for the mode of grouped data, use the formulaMo = Lmo+{( fmo – f1 )/( 2fmo – f1 – f2 )}i where, Lmo is the lower class boundary of the modal class, fmo is the frequency of the modal class, f1 is the frequency of the class preceding the modal class, f2 is the frequency of the class after the modal class, and i is the class size. CONTINUE

  30. Let’s Practice! The following distribution gives the number of hours allotted by 50 students to do their assignments in a week. Find the modal hour. SOLUTION

  31. Modal Class : Lmo : fmo : f1 : f2 : i :

  32. Modal Class : Lmo : 9 – 12 fmo : f1 : f2 : i :

  33. Modal Class : Lmo : 9 – 12 8.5 fmo : f1 : f2 : i :

  34. Modal Class : Lmo : 9 – 12 8.5 14 fmo : f1 : f2 : i :

  35. Modal Class : Lmo : 9 – 12 8.5 14 12 fmo : f1 : f2 : i :

  36. Modal Class : Lmo : 9 – 12 8.5 14 12 10 fmo : f1 : f2 : i :

  37. Modal Class : Lmo : 9 – 12 8.5 14 12 10 4 fmo : f1 : f2 : Compute the mode i :

  38. Mo = 8.5 + {[14 – 12] / [2(14) – 12 -10]}4 = 8.5 + (2/6)4 = 8.5 + 1.33 = 9.83 CONTINUE

  39. More Practice? SKIP Find the mode using the frequency distribution of the heights of 40 students. SOLUTION

  40. Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3 = 63.5 + (2/3)3 = 63.5 + 2 = 65.5 NEXT

  41. EVALUATE YOURSELF Find the mode of 20 students whose scores on a 15-point test are given in the following distribution: SOLUTION

  42. Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3 = 6.5 + (4/7)3 = 6.5 + 1.714 = 8.21 NEXT

  43. Try Another One A sample of 40 tourists traveled to Puerto Galera with the distribution based on the length of their stay (in years). Find the mode. SOLUTION

  44. Mo = 0.5 + {[8 – 0] / [2(8) – 0 - 7]}8 = 0.5 + (8/9)8 = 0.5 + 7.1 = 7.1

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