The document explains how to calculate measures of position, specifically deciles for grouped data, and provides a formula for determining these values. An example using mathematics test scores of 50 students illustrates the calculations needed to find the 7th decile, concluding that 70% of students scored less than or equal to 39.14. The objectives include illustrating quartiles, deciles, and percentiles, and calculating specified measures of position.

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. DECILES FOR GROUPED DATA
•DECILES ARE THOSE VALUES THAT DIVIDE THE TOTAL
FREQUENCY INTO 10 EQUAL PARTS.

4. THE DECILES FOR GROUPED DATA
1. THE FOLLOWING FORMULA IS USED IN FINDING THE DECILES
OF GROUPED DATA
kN
cfb-
Dk = LB +
10
fDK[ ]i
Where: LB = lower boundary of Dk class
N = total frequency
cfb = cumulative frequency of the
class before the Dk class
fDk = frequency of the Dk class
i = size of the class interval
k = nth quartile, where n = 1, 2, 3, … , 9

5. THE MEASURE OF POSITION
DECILE FOR GROUPED DATA
2. FORMULA TO CALCULATE THE DK CLASS
Dk class=
kN
10
Where: N = total frequency
k = nth quartile, where n = 1, 2, 3, 4, 5, 6, 7, 8, & 9

6. THE MEASURE OF POSITION
DECILE FOR GROUPED DATA
EXAMPLE
CALCULATE THE 7TH DECILE 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
DECILE 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
DECILE 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
DECILE FOR GROUPED DATA
D7 class=
7N
10
STEP 2.A: CALCULATE THE D7 CLASS
N = 50 k = 7Given:
D7 class =
7(50)
10
= 35
This means that we need to find the class interval where
the 35th score is contained

10. THE MEASURE OF POSITION
DECILE FOR GROUPED DATA
STEP 2.B: LOCATE THE CLASS INTERVAL WHERE THE D7
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)
D7 class
The D7 class is class interval 36-40
N = 50
cfb = 27
fD7 = 11
LB = 35.5
i = 5
Σ f = 50
Cfb =
fD7 = LB =
i = 5

11. THE MEASURE OF POSITION
DECILE FOR GROUPED DATA
STEP 2: SOLVE D7 USING THE FORMULA
7N
cfb-
D7 = LB +
10
fD7[ ]i
N = 50
cfb = 27
fD7 = 11
LB = 35.5
i = 5

12. THE MEASURE OF POSITION
DECILE FOR GROUPED DATA
Therefore, 70% of the students got a score less than or equal to 39.14
7(50)
27-
D7 = 35.5 + 10
11[ ]5
Given: N = 50
cfb = 27
fD7 = 11
LB = 35.5
i = 5
D7 = 39.14 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