Q4_Week 3-4_Measures of Position (Grouped Data).pptx

It discusses the frequency distribution table. Showing the components of FDT which are needed in the computation of measures of positions for grouped data. It gives examples for each quantiles such as quartiles, deciles and percentiles. It also provides activity that students may answer after the discussion

1. Measures of Position ( Grouped Data ) by: SHARON A. MIRANDA Q4_WEEK 3-4

2. QUARTILES

3.   where: LB = lower boundary of the N = total frequency = cumulative frequency of the class before the = frequency of the = size of the class interval = nth quartile, where n= 1, 2, and 3  

4. Erika’s teacher summarized the achievement test results of her class in the table. If Erika belongs to this class and her score is 76, does she belong to upper 25% of her class?

5. Achievement Test Results in Mathematics of 40 students

6. Scores Frequency (f) 90 – 99 3 80 – 89 4 70 – 79 6 60 – 69 11 50 – 59 8 40 – 49 5 30 - 39 3 n= 40

7. Scores Frequency (f) Lower Boundary Upper Boundary 90 – 99 3 89.5 99.5 80 – 89 4 79.5 89.5 70 – 79 6 69.5 79.5 60 – 69 11 59.5 69.5 50 – 59 8 49.5 59.5 40 – 49 5 39.5 49.5 30 - 39 3 29.5 39.5 n= 40

8. Scores Frequency (f) Lower Boundary Upper Boundary less than cf (< cf ) 90 – 99 3 89.5 99.5 80 – 89 4 79.5 89.5 70 – 79 6 69.5 79.5 60 – 69 11 59.5 69.5 50 – 59 8 49.5 59.5 40 – 49 5 39.5 49.5 30 - 39 3 29.5 39.5 n= 40 3 8 16 27 33 37 40 + + + + + +

9. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40 Identify the            

10. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40              

11. Erika’s teacher summarized the achievement test results of her class in the table. If Erika belongs to this class and her score is 76, does she belong to upper 25% of her class? This means that 75% of the class has a score of equal or less than 75. Since Erika’s score is 76, she belongs to upper 25% of her class.  

12. Using the same data in number 1, f ind Decile 5 and interpret the data.

13. DECILE

14. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40 Identify the           17  

15. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40             50% of the class has a score of equal or less than 63.  

16. Using the same data in number 1, f ind Percentile 90 and interpret the data.

17. PERCENTILE

18. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40 Identify the            

19. Scores (f) LB (< cf ) 90 – 99 3 89.5 40 80 – 89 4 79.5 37 70 – 79 6 69.5 33 60 – 69 11 59.5 27 50 – 59 8 49.5 16 40 – 49 5 39.5 8 30 - 39 3 29.5 3 n= 40             90% of the class has a score of equal or less than 87.

20. The following is a distribution for the numbe r of Grade 10 students in 60 schools both in public and private. Calculate the lower quartile, 6 th decile and 85 th percentile.

21. Number of Students Frequency (f) 26- 30 2 31- 35 6 36- 40 5 41- 45 12 46- 50 14 51- 55 10 56- 60 11

22. Number of Students Frequency (f) 56 – 60 11 51 – 55 10 46 – 50 14 41 – 45 12 36 – 40 5 31 – 35 6 26 – 30 2 n= 60

23. Scores Frequency (f) Lower Boundary Upper Boundary 56 – 60 11 55.5 60.5 51 – 55 10 50.5 55.5 46 – 50 14 45.5 50.5 41 – 45 12 40.5 45.5 36 – 40 5 35.5 40.5 31 – 35 6 30.5 35.5 26 – 30 2 25.5 30.5 n= 60

24. Scores Frequency (f) Lower Boundary Upper Boundary less than cf (< cf ) 56 – 60 11 55.5 60.5 51 – 55 10 50.5 55.5 46 – 50 14 45.5 50.5 41 – 45 12 40.5 45.5 36 – 40 5 35.5 40.5 31 – 35 6 30.5 35.5 26 – 30 2 25.5 30.5 n= 60 2 8 13 25 39 49 60 + + + + + +

25. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60 Identify the            

26. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60              

27. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60 Identify the            

28. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60            

29. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60 Identify the            

30. Scores (f) LB (< cf ) 56 – 60 11 55.5 60 51 – 55 10 50.5 49 46 – 50 14 45.5 39 41 – 45 12 40.5 25 36 – 40 5 35.5 13 31 – 35 6 30.5 8 26 – 30 2 25.5 2 n= 60            

31. Learning Task 1 (Week 3) Given the same data (example 1), find and interpret the percentile 75. (10 pts.) Scores Frequency (f) Less than cf 90 – 99 3 40 80 – 89 4 37 70 – 79 6 33 60 – 69 11 27 50 – 59 8 16 40 – 49 5 8 30 - 39 3 3

32. Learning Task 2 (Week 4) Answer the following: The frequency distribution presented below gives the ages of the members of the families in Barangay Hugo Perez. 1. How many members are there in Brgy . Hugo Perez? (3 pts.) 2. Find the less than cf of the given data. (5 pts) 3. In which decile or percentile do we find the 30% of the members of the Brgy . Hugo Perez? (2 pts.)

33. 4. If Carlos is one of the members of the community and his age is 56, does he belong to upper 20% age group? (Use Percentile 30, and interpret the data) (10 pts.) Ages Frequency Less than cf 81 – 90 7   71 – 80 4   61 – 70 13   51 – 60 17   41 – 50 27   31 – 40 16   21 – 30 43   11 – 20 35   1 - 10 38