1. 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

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: 1. Compute the mode for grouped data. 2. 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. 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. 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

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? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 75 – 79 12 70 – 74 3 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? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 (Modal Class) 75 – 79 12 70 – 74 3 ANSWER

13. ANSWER: L mo = 74.5 CONTINUE

14. 3. What is the frequency of the modal class? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 (Modal Class) 75 – 79 12 70 – 74 3 ANSWER

15. ANSWER: f mo = 12 CONTINUE

16. 4. What is the frequency of the class preceding the modal class? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 (Modal Class) 75 – 79 12 70 – 74 3 ANSWER

17. ANSWER: f 1 = 8 CONTINUE

18. 5. What is the frequency of the class after the modal class? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 (Modal Class) 75 – 79 12 70 – 74 3 ANSWER

19. ANSWER: f 2 = 3 CONTINUE

20. 6. What is the class size? Grades Number of students 90 – 94 2 85 – 89 5 80 – 84 8 75 – 79 12 70 – 74 3 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 74.5128 835 CONTINUE

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

24. 12 is the frequency of the modal class (f mo )

25. 8 is the frequency of the class preceding the modal class (f 1 )

26. 3 is the frequency of the class after the modal class (f 2 ).

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 formula To solve for the mode of grouped data, use the formula Mo = L mo +{( f mo – f 1 )/( 2f mo – f 1 – f 2 )}iwhere, L mo is the lower class boundary of the modal class, f mo is the frequency of the modal class, f 1 is the frequency of the class preceding the modal class, f 2 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. Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4 SOLUTION

31. Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

32. 9 – 12 9 – 12 Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

33. 9 – 12 9 – 12 8.5 8.5 Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

34. 9 – 12 9 – 12 8.5 8.5 14 14 Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

35. 9 – 12 9 – 12 8.5 8.5 14 14 12 12 Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

36. 9 – 12 9 – 12 8.5 8.5 14 14 12 12 10 10 Modal Class : L mo : f mo : f 1 : f 2 : i : Hours Number of Students 1 - 4 9 5 - 8 12 9 - 12 14 13 - 16 10 17 - 20 4

37. 9 – 12 9 – 12 8.5 8.5 14 14 12 12 10 10 4 Modal Class : L mo : f mo : f 1 : f 2 : i : Compute the mode

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

39. More Practice? Find the mode using the frequency distribution of the heights of 40 students. Height(inches) No. of Students 52 – 54 2 55 – 57 4 58 – 60 3 61- 63 8 64 – 66 10 67 – 69 9 70 - 72 4 SKIP SOLUTION

40. Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3 = 63.5 + (2/3)3 = 63.5 + (2/3)3 = 63.5 + 2 = 63.5 + 2 = 65.5 = 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: Scores No. of Students 1 – 3 1 4 – 6 4 7 – 9 8 10 – 12 5 13 - 15 2 SOLUTION

42. Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3 = 6.5 + (4/7)3 = 6.5 + (4/7)3 = 6.5 + 1.714 = 6.5 + 1.714 = 8.21 = 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. Length of Stay (years) No. of Tourists 1 – 8 8 9 – 16 7 17 – 24 5 25 – 32 6 33 - 40 5 SOLUTION

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