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 25TH PERCENTILE AND 82ND 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
P25 class=
25N
100
STEP 2.A: CALCULATE THE P25 CLASS
N = 50 k = 25Given:
=
25(50)
100
=12.5
This means that we need to find the class interval where
the 12.5th score is contained

10. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE P25
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)
P25 class
The P25 class is class interval 26-30
N = 50
cfb = 6
fP25 = 12
LB = 25.5
i = 5
Σ f = 50
Cfb =
fP25 = LB =
i = 5

11. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2: SOLVE P25 USING THE FORMULA
25N
cfb-
P25 = LB +
100
fP25[ ]i
N = 50
cfb = 6
fP25 = 12
LB = 25.5
i = 5

12. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
Therefore, 25% of the students got a score less than or equal to 28.21
25(50)
6-
P25 = 25.5 + 100
12[ ]5
Given: N = 50
cfb = 6
fP25 = 12
LB = 25.5
i = 5
P25 = 28.21 Final answer

13. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
P82 class=
82N
100
STEP 2.A: CALCULATE THE P82 CLASS
N = 50 k = 82Given:
=
82(50)
100
= 41
This means that we need to find the class interval where
the 41st score is contained

14. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE P82
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
(39th to 46th score)
P82 class
The P82 class is class interval 41-45
N = 50 cfb = 38
fP82 = 8 LB = 40.5
i = 5
Σ f = 50
Cfb =
fP82 = LB =
i = 5

15. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
STEP 2: SOLVE P82 USING THE FORMULA
82N
cfb-
P82 = LB +
100
fP82[ ]i
N = 50
cfb = 38
fP82 = 8
LB = 40.5
i = 5

16. THE MEASURE OF POSITION
PERCENTILE FOR GROUPED DATA
Therefore, 82% of the students got a score less than or equal to 42.38
82(50)
38-
P82 = 40.5 + 100
8[ ]5
Given: N = 50
cfb = 38
fP82 = 8
LB = 40.5
i = 5
P82 = 42.38 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