Deciles & Quartiles - Point Measures

Assessment

1. Point Measures Prepared by: Sweet Charey Lou T. Mapindan

2. Point Measures Quartiles Deciles

3. Deciles Deciles are   nine partitional values  of the data or the given set of observation into ten equal parts. These 9 values are represented by D₁, D₂, D₃, D₄, D₅, D₆, D₇, D₈ and D₉ . They  shows the 10%, 20%, 30 %, 40%, 50%, 60%, 70%, 80% and 90%

4. Deciles for Ungrouped Data D 1 = value of D 2 = value of D 9 = value of   Formula:

5. Deciles for Ungrouped Data Solution: First, arrange the scores in ascending order. Example: Find the 7 th Decile or D 7 of the following test scores of a random sample of 10 students. 36 43 41 29 16 24 34 21 19 29

6. Ascending order: 16 19 21 24 29 29 34 36 41 43 Formula: D 7 = value of   D 7 = ? D 7 = D 7 is the 8 th element Therefore, D 7 = 36  

7. Deciles for Grouped Data Those values of the distribution that divided total frequency to ten groups. Md = P 50 = D 5 = Q 2

8. Md = P 50 = D 5 = Q 2 Md = LL (   LL is the real lower limit of the median class, is the total number of cases in the distribution, is the number of cases below the median class, is the number of cases within the median class, and is the size of class interval ( = number of scores in a class or group)  

9. Illustration: 6 th decile (D 6 ) Locate the 6 th decile in the following data, that is, find the value that will divide the ordered set of scores into two subgroups, the upper 40% and the lower 60%. X f cf 27-29 1 57 24-26 3 56 21-23 6 53 18-20 10 47 15-17 9 37 12-14 11 28 9-11 10 17 6-8 3 7 3-5 3 4 0-2 1 1 n = 57

10. To estimate D 6 , the modified formula would be D 6 = (   is the real lower limit of the D 6 class, is the total number of cases in the distribution, is the number of cases below the D 6 class, is the number of cases within the D 6 class, and is the size of class interval ( = number of scores in a class or group)  

11. D 6 is = (0.6)(57) = 34.2   From the cf column, the 34.2 nd case falls in the interval (15-17), thus, the D 6 class is the interval (15-17), and = 28 = 9  

12. Using the modified formula: D 6 = (   = 14.5+2.06667 = 16.57   This means that students with scores greater than 16.57 belong to the upper 40% of the class and students with scores less than 16.57 belong to the lower 60% of the class.

13. Quartiles Quartiles are the score points which divide a distribution into four equal parts. 25% 50% 75% 100% Lower Quartile Middle Quartile Upper Quartile Q 1 Q 2 Q 3

14. Quartiles for Ungrouped Data Formula:

15. Example: Following is the data of marks obtained by 20 students in a test of statistics. Find Quartiles Q 1 Q 2 Q 3 : 53 74 82 42 39 20 81 68 58 28 67 54 93 70 30 55 36 37 29 61 20 28 29 30 36 37 39 42 53 54 55 58 61 67 68 70 74 81 82 93 Ascending order n = 20

16. Quartiles for Grouped Data Illustration: 3 rd quartile (Q 3 ) Locate the 3 rd quartile ( Q 3 ) in the following data, that is, find the value that will divide the ordered set of scores into two subgroups, the upper 25% and the lower 75%. X f cf 27-29 1 57 24-26 3 56 21-23 6 53 18-20 10 47 15-17 9 37 12-14 11 28 9-11 10 17 6-8 3 7 3-5 3 4 0-2 1 1 n = 57

17. To estimate Q 3 , the modified formula would be Q 3 = (   is the real lower limit of the Q 3 class, is the total number of cases in the distribution, is the number of cases below the Q 3 class, is the number of cases within the Q 3 class, and is the size of class interval ( = number of scores in a class or group)  

18. The position of Q 3 is   From the cf column, the 42.75 th case falls in the interval (18-20), thus, the Q 3 class is the interval (18-20), and = 37 = 10  

19. = 17.5+1.725 = 19.225   Using the modified formula: Q 3 = (   This means that students with scores greater than 19.225 belong to the upper 25% of the class and students with scores less than 19.225 belong to the lower 75% of the class.

20. Exercises: 1. Find the 1 st quartile, 2 nd quartile, and third quartile, given the scores of 10 students in their Mathematics quiz. 38 43 56 55 25 27 25 39 40 45 2 . Find the 6th decile, 7th decile, and 9th decile, given the scores of 10 students in their Mathematics quiz.

21. Exercises: 3. Find D 2 , D 3 , D 8. 4 . Find Q 1 , Q 2 , Q 3 .

22. Thank you for listening! God bless. 