QUARTILES, DECILES AND PERCENTILES

WORLD OF MATH

1. REPORTER : MARIA KATRINA S. MACAPAZ

2. ORGANIZING DATA USING: PERCENTILES *QUARTILES *DECILES

3. * PERCENTILES -is a measure used to indicate the value below which a given percentage of observations fall . Let us call this P=%. Example: (100-P)%. - The 90 percentile is the value below with 90 % of observations may be found.

4. * PERCENTAGES: Data Set: 1, 2 ,3, 4 ,5 How many numbers are even? Percentage= # meeting Characteristics of interest *100 total number of observations Percentage= * 100=40%  

5. PENCENTILE A value below which a certain percentage of observations lie. Data set: 2,2,3,4,5,5,5,6,7,8,8,8,8,8,9,9, 10 ,11,11,12 What is the percentile ranking of “10”? Percentile rank of x= # of values below *100 n Percentile rank of ‘10’ = *100= 80%  

6. Data set: 2,2,3,4,5,5,5,6,7,8,8,8,8,8,9,9,10,11,11,12 What Value Exist at the percentile ranking of 25 %? Value #= (n+1) Value # = (20 +1) = 5. 25 There is no “5.25 th ”, so I take the average of the 5 th & 6 th values to find what value exist at the 25 th percentile . = 5  

7. QUARTILES

8. QUARTILES

9. FINDING MEDIAN , Q1, Q2 in a short cut way: DATA SET: 2,8,5,3,10,6,7,9,1 ARRANGED ORDER: 1,2,3,5,6,7,8,9,10 1,2,3,5 , 6, 7,8,9,10 MEDIAN = =2.5 = = 8.5  

10. Raw or Ungrouped data: First arrange the given data in the incrasing order and use the formula for and quartile deviation. Q.D is given by: Q.D = Where: ( ) th item and ( ) th item  

11. Compute quartiles for the data given: 25,18,30,8,15,5,10,35,40,45 Arrange data: 5,8,10,15,18,25,30,35,40,45 ) th item =( th item =(2.75) th item =2 nd item + ( ) (3 rd item- 2 nd item) =8 + (10-8) ==8 + x 2 = 8+ 1.5 =9.5  

12. Arrange data: 5,8,10,15,18,25,30,35,40,45 3( ) th item = ( th item =3x(2.75) th item = (8.25) th item =8 th item + (9 th item-8 th item) =35 + (40-35) =35+ 1.25= 36.25 =36.25  

13. QUARTILE DEVIATION Q.D= =______ Q.D= = 13.37  

14. DECILES The values which divide an array into ten equal parts are called deciles . The first, second,…… ninth deciles by respectively. The fifth decile ( corresponds to median. The second, fourth, sixth and eighth deciles which collectively divide the data into five equal parts are called quintiles .

15. Deciles for Ungrouped Data: Deciles for ungrouped data will be calculated from the following formulae ; =value of ( th item = Value of th item = Value of th item  

16. For Example: We will calculate second, third and seventh deciles from the following array of data. 20 28 29 30 36 37 39 42 53 54 55 58 61 67 68 70 74 81 82 93

17. = Value of th item = th item = 4.2 th item from below = The value of the 4 th item is 30 and that of the 5 th item is 36. Thus the second decile is a value 0.2th of the way between 30 and 36. The fifth decile will be 30 + 6(0.2) = 31.2 . Therefore, = 31.2.  

18. = Value of th item = th item =6.3th item from below The value of the 6 th item is 37 and that of the 7 th item is 39. Thus the third decile is 0.3th of the way between 37 and 39. The third decile will be 37 + 2(0.3) = 37.6. Hence, = 37.6 .  

19. = Value of th item = th item =14.7 th item from below The value of the 14 th item is 67 and that of the 15 th item is 68. Thus the 7 th decile is 0.7 th of the way between 67 and 68, which will be as 6 7 + 1( 0.7) = 67.7. Therefore, = 67.7 .  

20. SO IF YOU WANT TO ORGANIZE YOUR DATA BY THE USE OF (PERCENTILES, QUARTILES, DECILES) JUST REMEMBER THE FOLLOWING EQUATIONS: Percentile rank of x= # of values below *100 n Q.D = *Where : ( ) th item and ( ) th item * =value of ( th item