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1. OBJECTIVES Define Percentile in statistic Calculate the Percentile for Grouped data Relate the concept of measure of position of Percentile for Group data in real-life situations.

2. MEASURES OF POSITION PERCENTILES FOR GROUPED DATA RAPHAEL V. PEREZ

3. Classroom Rules Please Read. 1. Be respectful 2. Participate Actively 3. Ask Questions when things are not clear 4.Speak respectfully and avoid using offensive language

4. N F E O E P I E R C L T E P R C E N E I L T

5. E M V S U D A C S R E I E M A S U R E S

6. I S E T N O U R I P E O P S I I T O N O

7. Early on, you have already learned that: kth quartile denoted by Q k , kth decile denoted by D k , are computed, respectively, as follows: Measures of Position: Percentile for Grouped Data Q k = LB +   - cf b f QK i D k = LB +   - cf b f DK i and

8. What will be the formula for the kth percentile? Measures of Position: Percentile for Grouped Data Q k = LB +   - cf b f QK i D k = LB +   - cf b f DK i and if: P k = LB +   - cf b f PK i Then,

9. THE PERCENTILE FOR GROUPED DATA The percentile is ninety-nine score points which divide a distribution into one 100 equal parts Measures of Position: Percentile for Grouped Data

10. THE kth PERCENTILE FORMULA FOR GROUPED DATA Measures of Position: Percentile for Grouped Data P k = LB +   - cf b f PK i LB = lower boundary of the kth percentile class total frequency   cf b = cumulative frequency before the percentile class f PK = frequency of the percentile class i = the interval or class width nth percentile where = 1, 2, 3,…..97, 98 and 99   Where:

11. To determine the percentile class in the Frequency Distribution Table: Measures of Position: Percentile for Grouped Data Step 1: Compute for the Position to determine percentile class   Position of P K : Step 2: Set the given facts for the identified Percentile Class. Like : LB - the lower boundary of a percentile class cf b - cumulative frequency before the percentile class - the position of a percentile class f PK - frequency of a percentile class i - the class width or interval  

12. To determine the percentile class in the Frequency Distribution Table: Measures of Position: Percentile for Grouped Data Step 3: Set the formula and substitute the variables using the given facts and then, evaluate. Step 4: Write the analysis of the value of the Percentile Class

13. Example: What should be the score to exceed the exact 65% (65th percentile) of the students? Measures of Position: Percentile for Grouped Data Class score Frequency(f) LB CF 46-50 4 41-45 8 36-40 11 31-35 9 26-30 12 21-25 6

14. Example: What should be the score to exceed the exact 65% (65th percentile) of the students? Measures of Position: Percentile for Grouped Data Class score   Frequency(F) LB CF 46-50 4 45.5 50 41-45 8 40.5 46 36-40 11 35.5 38 31-35 9 30.5 27 26-30 12 25.5 18 21-25 6 20.5 6

15. Calculate the 65 th Percentile of the Mathematics Test Scores of 50 Students.

16. Compute for the Position of the 65th Percentile Class or P 65 Measures of Position: Percentile for Grouped Data SCORES (Class Interval) Frequency ( f ) LB <cf 46-50 4 45.5 50 41-45 8 40.5 46 36-40 11 35.5 38 31-35 9 30.5 27 26-30 12 25.5 18 21-25 6 20.5 6 N = 50   Position of P 65 : :   :   : 32.50 or 33th The 33 position is between the cumulative frequency 27th and 38th. Use the class 36-40 P 65

17. Step 2: Set the given facts for 65th Percentile Class or P 65 Measures of Position: Percentile for Grouped Data SCORES (Class Interval) Frequency ( f ) LB <cf 46-50 4 45.5 50 41-45 8 40.5 46 36-40 11 35.5 38 31-35 9 30.5 27 26-30 12 25.5 18 21-25 6 20.5 6 N = 50 P 65 Given: LB = 35.5 N = 50 cf b = 27 f P65 = 11 i = 5 cf b = LB = f P65 =

18. Step 3 and 4: Set the formula for P 65 ,substitute and evaluate. Write the final answer and put the analysis. Measures of Position: Percentile for Grouped Data Given: LB = 35.5 N = 50 cf b = 27 f P65 = 11 i = 5 P k = LB +   - cf b f PK i Formula: P 65 = 35.5 +   - 27 11 5

19. Measures of Position: Percentile for Grouped Data P 65 = 35.5 + 33 - 27 11 5 P 65 = 35.5 + 6 11 5 P 65 = 35.5 + 0.5 5 P 65 = 35.5 + 2.5 P 65 = 38.0 Analysis: 65% of the students got a score below 38 and 35% of the students got a score above 38.