This document discusses how to calculate quartiles, deciles, and percentiles from a set of grouped data. It provides a formula to find the quartiles of grouped data which involves determining the lower boundary, cumulative frequency, and frequency of the quartile class. An example is shown calculating the first, second, and third quartiles of mathematics test scores from 50 students grouped into classes. The first quartile is calculated to be 28.21 using the provided formula.

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. QUARTILE FOR GROUPED DATA
•THE QUARTILES ARE THE SCORE POINTS WHICH
DIVIDE A DISTRIBUTION INTO FOUR EQUAL PARTS.

4. THE QUARTILE FOR GROUPED DATA
1. THE FOLLOWING FORMULA IS USED IN FINDING THE QUARTILES
OF GROUPED DATA
kN
cfb-
Qk = LB +
4
FQK[ ]i
Where: LB = lower boundary of Qk class
N = total frequency
cfb = cumulative frequency of the
class before the Qk class
FQk = frequency of the Qk class
i = size of the class interval
k = nth quartile, where n = 1, 2, and 3

5. THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
2. FORMULA TO CALCULATE THE QK CLASS
Qk class=
kN
4
Where: N = total frequency
k = nth quartile, where n = 1, 2, and 3

6. THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
EXAMPLE
CALCULATE THE Q1, Q2, AND Q3 IF 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
QUARTILE 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
QUARTILE 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
QUARTILE FOR GROUPED DATA
Q1 class=
N
4
STEP 2.A: CALCULATE THE Q1 CLASS
N = 50 k = 1Given:
Q1 class =
50
4
=12.5
This means that we need to find the class interval where
the 12.5th score is contained

10. THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE Q1
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)
Q1 class
The Q1 class is class interval 26-30
N = 50
cfb = 6
fQ1 = 12
LB = 25.5
i = 5
Σ f = 50
Cfb =
fQ1 = LB =
i = 5

11. THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
STEP 2: SOLVE Q1 USING THE FORMULA
N
cfb-
Q1 = LB +
4
FQ1[ ]i
N = 50
cfb = 6
fQ1 = 12
LB = 25.5
i = 5

12. THE MEASURE OF POSITION
QUARTILE FOR GROUPED DATA
Therefore, 25% of the students have a score less than or equal to 28.21
50
6-
Q1 = 25.5 + 4
12[ ]5
Given: N = 50
cfb = 6
fQ1 = 12
LB = 25.5
i = 5
Q1 = 28.21 Final answer

13. 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.

14. THANK YOU
EDUCATIONAL PROJAMS