Percentile and percentile rank

The presentation talks about concept, methods of calculation and usages of percentile and percentile rank

1. Percentile and Percentile Rank Gautam Kumar Assistant Professor University Department of Teacher Education Utkal University, Bhubaneswar

2. PERCENTILE Introduction: Percentile (centile) is used to indicate relative position of a single item or an individual with reference to the group to which the item or individual belongs. It denotes the relative position of given score among other score. Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 2

3. PERCENTILE Definition: Percentile is a point on a score scale below which a given percent of cases lie. It is denoted by P n , where n is the number of percentile. P 1 is first percentile, which means it is a point on the given score below which 1% score lies. Means 99% score are above this point. P 15 is 15 th percentile, which means it is a point on the given score below which 15% score lies. Means 85% score are above this point. P 50 is 50 th percentile, which means it is a point on the given score below which 50% score lies. Means 50% score are above this point. It is also know as Median. Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 3

4. QUARTILES & DECILES Quartiles: A quartiles is the point on the score scale below which a given quarter of the cases lie. Deciles: A deciles is the point on the score scale below which a given decile of the cases lie. Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 4

5. QUARTILES & DECILES Formula for computation of Median So 1 st quartile 2 nd quartile 3 rd quartile   Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 5

6. QUARTILES & DECILES Formula for computation of Median So 1 st decile 5 th decile 8 th quartile and so on   Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 6

7. PERCENTILE Formula for computation of Median 1 st percentile 10 th percentile 25 th percentile 50 th percentile 25 th percentile   Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 7

8. PERCENTILE General formula for percentile Percentile, Where L=Lower limit of the percentile class (the class in which the given percentile may be suppose to lie) N=Total number of frequencies F=Total number of frequencies before percentile class f =Frequency of percentile class i =Size of the class interval p =No. of percentile which has to be computed   Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 8

9. PERCENTILE Computation of Quartile, Decile and Percentile Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 9 Scores f 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=24 3 rd Quartile Here 3N/4 = 24*3/4 = 18 Here on adding frequencies from below, we find that in the class interval 50-59, quartile 18 will lie So, L=49.5, F=17, f=2 and i = 10 Hence  

10. PERCENTILE Computation of Quartile, Decile and Percentile Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 10 Scores f 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=24 25 th Percentile 24/100 = 0.24  

11. PERCENTILE RANK Percentile Rank: Percentile rank is the number representing the percentage of the total number of cases lying below the given scores. If in a class of 50 students. A student (say student ‘X’) secured a score of 70 on achievement test. There are 45 other students whose scores falls below the score 70. Therefore 45 out of 50 (45/50 x 100 = 90%) student lie below the score 45. Hence, 45 will be termed as 90 th percentile of the above data. The position student ‘X’ enjoys in relation to the other students may be seen by the fact that the score 45 out of 50 or 90% of the students falls below the score of student ‘X’. Which means student ‘X’ is better than 90% of students in the calss . From the above we can conclude that score 70 secured by student ‘X’ has a percentile rank of 90. Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 11

12. PERCENTILE RANK Calculation of Percentile from ungrouped data Scores are 12, 20, 25, 15, 8, 32, 28, 35, 22, 44, 36, 17, 29, 13, 9, 37, 40, 21, 10, 42 What is the percentile rank of 17? Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 12 Scores Rank 44 1 42 2 40 3 37 4 36 5 35 6 32 7 29 8 28 9 25 10 Scores Rank 22 11 21 12 20 13 17 14 15 15 13 16 12 17 10 18 9 19 8 20 Percentile Rank (PR) = Where N = Total no of individual in score group R = Rank position of the score of an individual whose percentile rank is to be calculated = 32.5 or 32 The percentile rank of the score 17 is 32.  

13. PERCENTILE RANK Calculation of Percentile from grouped data Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 13 Scores Frequency 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=20 First Method Calculate the percentile rank of score 22 By adding the frequencies from below we see that upto the score 19.5, i.e. the upper limit of the class 10-19, 5 cases lie. Our requirement here is to find out the number of cases that lie below the score 22. Now by observing the frequency distribution, we see that in the class interval 20-29, 10 scores are shared by 4 individuals. So, an interval of 10 is shared by 4 individuals, therefore, an interval of 2.5 is hared by 4/10*2.5=1 individual

14. PERCENTILE RANK Calculation of Percentile from grouped data Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 14 Scores Frequency 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=20 Therefore, upto the score 22, 5+1 = 6 cases lie So the required percentile rank is 6*100/24=25

15. PERCENTILE RANK Calculation of Percentile from grouped data Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 15 Scores Frequency 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=20 Second Method Calculate the percentile rank of score 22 Where: PR=Percentile rank F=Cumulative frequency below the interval containing score X X=Score for which we want to calculate percentile rank L=Actual lower limit of the interval containing X i =Size of the class interval f =Frequency of the interval containing X N=Total number of cases in the given frequency distribution  

16. PERCENTILE RANK Calculation of Percentile from grouped data Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 16 Scores Frequency 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N=20 Here F=Cumulative frequency below the interval containing score X L=Actual lower limit of the interval containing X i =Size of the class interval f =Frequency of the interval containing X N=Total number of cases in the given frequency distribution F=5 X=22 L=19.5 i =10 f =4 N=24 = 25  

17. USE OF THE PERCENTILE It gives the relative position of the scores. It may be used for comparison such as Two or more students belonging to two or more sections, classes or schools The performance of tow or more classes, sections or schools. The performance of individual if tested under two or more different testing conditions in terms of possession of some attributes or traits. Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 17

18. Q & A Tuesday, 9 June, 2020 Gautam I UUDTE I Utkal University 18