This document discusses how to calculate percentiles for grouped data. It provides a formula to find the kth percentile which takes into account the lower boundary of the class, cumulative frequency below the class, frequency of the class, and class interval size. The document also works through an example calculating the 65th and 32nd percentiles for a set of math test score data grouped into classes. It is found that the 65th percentile is 38 and the 32nd percentile is 29.67.

2. OBJECTIVES
•ILLUSTRATE THE FOLLOWING MEASURES OF
POSITION: QUARTILES, DECILES AND PERCENTILES
•CALCULATE SPECIFIED MEASURE OF POSITION (E.G.
90TH PERCENTILE) OF A SET OF DATA.

3. PERCENTILE FOR GROUPED DATA
•THE PERCENTILE OF GROUPED DATA IS USED TO
CHARACTERIZE VALUES ACCORDING TO THE
PERCENTAGE BELOW THEM.

4. THE PERCENTILE FOR GROUPED DATA
1. THE FOLLOWING FORMULA IS USED IN FINDING THE PERCENTILE
OF GROUPED DATA
kN
cfb-
Pk = LB +
100
fPK[ ]i
Where: LB = lower boundary of Pk class
N = total frequency
cfb = cumulative frequency of the
class before the Pk class
fPk = frequency of the Pk class
i = size of the class interval
k = nth quartile, where n = 1, 2, 3, … , 99

5. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
2. FORMULA TO CALCULATE THE PK CLASS
Pk class=
kN
100
Where: N = total frequency
k = nth quartile, where n = 1, 2, 3, 4, …, 97, 98, & 99

6. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
EXAMPLE
CALCULATE THE 65TH PERCENTILE AND 32ND PERCENTILE OF
THE MATHEMATICS TEST SCORES OF 50 STUDENTS
SCORES FREQUENCY
46-50 4
41-45 8
36-40 11
31-35 9
26-30 12
21-25 6

7. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 1.A: DETERMINE THE LOWER BOUNDARIES
SCORES FREQUENCY Lower Boundaries
(LB)
46-50 4
41-45 8
36-40 11
31-35 9
26-30 12 25.5
21-25 6 20.5
To solve for LB
subtract 0.5 to the
smallest number per
class interval
21 – 0.5 = 20.5
30.5
35.5
40.5
45.5

8. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 1.B: DETERMINE THE CUMULATIVE FREQUENCY
SCORES FREQUENCY Lower Boundaries
(LB)
Less than
Cumulative
Frequency (<cf)
46-50 4 45.5
41-45 8 40.5
36-40 11 35.5
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6 Copied from the frequency
6 + the frequency of the class interval
18 + the frequency of the class interval
38
46
50

9. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
P65 class=
65N
100
STEP 2.A: CALCULATE THE P65 CLASS
N = 50 k = 7Given:
P65 class =
65(50)
100
=32.5
This means that we need to find the class interval where
the 32.5th score is contained

10. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE P65
CLASS IS SITUATED
SCORES FREQUENCY Lower Boundaries
(LB)
Less thanCumulative
Frequency (<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
(28th to 38th score)
P65 class
The P65 class is class interval 36-40
N = 50
cfb = 27
fP65 = 11
LB = 35.5
i = 5
Σ f = 50
Cfb =
fP65 = LB =
i = 5

11. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2: SOLVE P65 USING THE FORMULA
65N
cfb-
P65 = LB +
100
fP65[ ]i
N = 50
cfb = 27
fP65 = 11
LB = 35.5
i = 5

12. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
Therefore, 65% of the students got a score less than or equal to 38
65(50)
27-
P65 = 35.5 + 100
11[ ]5
Given: N = 50
cfb = 27
fP65 = 11
LB = 35.5
i = 5
P65 = 38 Final answer

13. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
P32 class=
32N
100
STEP 2.A: CALCULATE THE P32 CLASS
N = 50 k = 7Given:
P32 class =
32(50)
100
= 16
This means that we need to find the class interval where
the 16th score is contained

14. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE P32
CLASS IS SITUATED
SCORES FREQUENCY Lower Boundaries
(LB)
Less thanCumulative
Frequency (<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
(7th to 18th score)
P32 class
The P32 class is class interval 26-30
N = 50
cfb = 6
fP32 = 12
LB = 25.5
i = 5
Σ f = 50
Cfb =
fP32 = LB =
i = 5

15. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2: SOLVE P32 USING THE FORMULA
32N
cfb-
P32 = LB +
100
fP32[ ]i
N = 50
cfb = 6
fP32 = 12
LB = 25.5
i = 5

16. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
Therefore, 32% of the students got a score less than or equal to 29.67
32(50)
6-
P32 = 25.5 + 100
12[ ]5
Given: N = 50
cfb = 6
fP32 = 12
LB = 25.5
i = 5
P32 = 29.67 Final answer

17. OBJECTIVES
•ILLUSTRATE THE FOLLOWING MEASURES OF
POSITION: QUARTILES, DECILES AND PERCENTILES
•CALCULATE SPECIFIED MEASURE OF POSITION (E.G.
90TH PERCENTILE) OF A SET OF DATA.

18. THANK YOU
EDUCATIONAL PROJAMS