Mode of Grouped Data - Math 7 (4th Quarter)
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This document discusses the concept of mode in grouped data. It provides examples of calculating the mode of different data sets. The mode is the value that occurs most frequently in a data set. For grouped data, the mode is calculated using a formula that considers the lower boundary of the modal class, the frequency of the modal class, and the frequencies of neighboring classes. Worked examples demonstrate applying this formula to frequency distributions to determine the modal value.
![Solution
Observe how the modal grade of the students is computed.
Mo = +80.5
[ 18 –___________________
2( ) – –
12
5
18 12 7
]
= 80.5 +
6
17
5
= 80.5 + 0.35 5
= 80.5 + 1.75
= 𝟖𝟐. 𝟐𝟓
Hence, the modal grade
of the students is 82.25.](https://image.slidesharecdn.com/carlolunamath74qmodeofgroupeddata-171208075744/85/Mode-of-Grouped-Data-Math-7-4th-Quarter-20-320.jpg)
Mode of Grouped Data - Math 7 (4th Quarter)
- 1. Mathematics 7 M e a s u r e s o f C e n t r a l T e n d e n c y MODE of Grouped Data MR. CARLO JUSTINO J. LUNA Malabanias Integrated School Angeles City
- 2. The only way to learn mathematics is to do mathematics.
- 3. Activity: What-You-Already-Know Find the mode of each of the following sets of numbers. a. 3, 2, 2, 4, 5, 1, 4, 6, 4 b. 77, 80, 90, 65, 77, 89, 80 c. 1987, 1993, 1985, 1990 Answer Answer Answer
- 4. a. 3, 2, 2, 4, 5, 1, 4, 6, 4 MODE: 4
- 5. b. 77, 80, 90, 65, 77, 89, 80 MODE: 77 and 80
- 6. c. 1987, 1993, 1985, 1990 MODE: No mode
- 7. For the next set of questions, refer to the given frequency distribution table of the grades of a group of students.
- 8. 1. Determine the modal class. Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5 Answer
- 9. Modal Class: 81 – 85 The modal class is the class with the highest frequency.
- 10. 2. What is the lower class boundary of the modal class? Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5 Answer Modal Class
- 11. lbmo = 80.5
- 12. 3. What is the frequency of the modal class? Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5 Answer Modal Class
- 13. fmo = 18
- 14. 4. What is the frequency of the class preceding the modal class? Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5 Answer Modal Class
- 15. fb = 12
- 16. 5. What is the frequency of the class after the modal class? Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5 Answer Modal Class
- 17. fa = 7
- 18. 6. What is the class size? Answer Grades Number of Students 91 – 95 3 86 – 90 7 81 – 85 18 76 – 80 12 71 – 75 5
- 19. i = 5
- 20. Solution Observe how the modal grade of the students is computed. Mo = +80.5 [ 18 –___________________ 2( ) – – 12 5 18 12 7 ] = 80.5 + 6 17 5 = 80.5 + 0.35 5 = 80.5 + 1.75 = 𝟖𝟐. 𝟐𝟓 Hence, the modal grade of the students is 82.25.
- 21. 80.5 is the lower class boundary of the modal class lbmo
- 22. 18 is the frequency of the modal class fmo
- 23. 12 is the frequency of the class before the modal class fb
- 24. 7 is the frequency of the class after the modal class fa
- 25. 5 is the class size i
- 26. How did we solve for the modal grade of the students? Can you give the formula for the mode of grouped data?
- 27. Formula To solve for the mode of grouped data, use the formula: 𝑀𝑜 = 𝑙𝑏 𝑚𝑜 + 𝑓𝑚𝑜 − 𝑓𝑏 2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎 𝑖 where 𝑙𝑏 𝑚𝑜 is the lower class boundary of the modal class 𝑓𝑚𝑜 is the frequency of the modal class 𝑓𝑏 is the frequency of the class before the modal class 𝑓𝑎 is the frequency of the class after the modal class 𝑖 is the class size
- 28. 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 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9
- 29. SOLUTION Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊:
- 30. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 SOLUTION
- 31. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 SOLUTION
- 32. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 14 SOLUTION
- 33. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 14 12 SOLUTION
- 34. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 14 12 10 SOLUTION
- 35. Hours Number of Students 17 – 20 4 13 – 16 10 9 – 12 14 5 – 8 12 1 – 4 9 Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 14 12 10 4 Compute the mode. SOLUTION
- 36. Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 9 – 12 8.5 14 12 10 4 SOLUTION = 8.5 + 2 6 4 𝑀𝑜 = 𝑙𝑏 𝑚𝑜 + 𝑓𝑚𝑜 − 𝑓𝑏 2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎 𝑖 = 8.5 + 14 − 12 2 14 − 12 − 10 4 𝑴𝒐 = 𝟗. 𝟖𝟐 = 8.5 + (0.33)4 = 8.5 + 1.32
- 37. MORE PRACTICE! Find the mode using the frequency distribution of the heights of 40 students. Height (inches) Number of Students 70 – 72 4 67 – 69 9 64 – 66 10 61 – 63 8 58 – 60 3 55 – 57 4 52 – 54 2SOLUTION SKIP
- 38. Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 64 – 66 63.5 10 8 9 3 SOLUTION = 63.5 + 2 3 3 𝑀𝑜 = 𝑙𝑏 𝑚𝑜 + 𝑓𝑚𝑜 − 𝑓𝑏 2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎 𝑖 = 63.5 + 10 − 8 2 10 − 8 − 9 3 𝑴𝒐 = 𝟔𝟓. 𝟓 = 63.5 + 2
- 39. EVALUATE YOURSELF Find the mode of 20 students whose scores on a 15-point test are given in the following distribution: Scores Number of Students 13 – 15 2 10 – 12 5 7 – 9 8 4 – 6 4 1 – 3 1 SOLUTION
- 40. Modal Class : 𝒍𝒃 𝒎𝒐: 𝒇 𝒎𝒐: 𝒇 𝒃: 𝒇 𝒂: 𝒊: 7 – 9 6.5 8 4 5 3 SOLUTION = 6.5 + 4 7 3 𝑀𝑜 = 𝑙𝑏 𝑚𝑜 + 𝑓𝑚𝑜 − 𝑓𝑏 2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎 𝑖 = 6.5 + 8 − 4 2 8 − 4 − 5 3 𝑴𝒐 = 𝟖. 𝟐𝟏 = 6.5 + 0.57 3 = 6.5 + 1.71
- 41. VALUING: Do you have a person or a thing in your life that you consider as a mode?
- 42. Mathematics 7 M e a s u r e s o f C e n t r a l T e n d e n c y MODE of Grouped Data MR. CARLO JUSTINO J. LUNA Malabanias Integrated School Angeles City