Prepared by: Patrick F. Maravilla DepEd Sorsogon

1. MEASURES OF
POSITION
PATRICK F. MARAVILLA
T-II

2. MEASURES OF POSITION
-are techniques that divide a set into equal
groups
-a method by which the position that a
particular data set can be identified.

3. MEASURES OF POSITION
1. Quartiles
2. Deciles
3. Percentiles

4. MEASURES OF POSITION FOR
UNGROUPED DATA

5. QUARTILES
 are the score points which divide a
distribution into four equal parts.

6. QUARTILE FOR UNGROUPED DATA
MENDENHALL AND SINCICH METHOD
-a method of finding the quartile value
-this method is developed by William
Mendenhall and Terry Sincich to find the
positionof the quartile position

7. QUARTILE FOR UNGROUPED DATA
To find Q1, Q2 and Q3, use the formula below:
Qk =
𝑘
4
(n + 1)
where
n = number of data/score
K = position of the quartile

8. QUARTILE FOR UNGROUPED DATA
Example:
1. The score of 7 students obtained in
Statistics quiz are: 7, 4, 3, 6, 7, 4, 8
Find:
a. Q1- Lower quartile
b. Q2 – Middle quartile
c. Q3 – Upper Quartile

9. QUARTILE FOR UNGROUPED DATA
Given: 3, 4, 4, 6, 7, 7, 8
Note: Scores must be arranged in ascending order
Qk =
𝑘
4
(n + 1) Qk =
𝑘
4
(n + 1) Qk =
𝑘
4
(n + 1)
Q1 =
1
4
( 7+ 1) Q2 =
2
4
( 7+ 1) Q3 =
3
4
( 7+ 1)
Q1 = 2nd Q2 = 4th Q3 = 6th
Q1 is 4 Q2 is 6 Q3 is 7

10. QUARTILE FOR UNGROUPED DATA
LINEAR INTERPOLATION
-a method of finding the quartile value.
-is a method of constructing new data points
within the range of an discrete set of known
data points.
-We need to use the interpolation if the value
of the position is in the decimal form.

11. QUARTILE FOR UNGROUPED DATA
Steps in using the interpolation method
1. Arrange the scores in ascending order
2. Locate the position of the score in the distribution
3. Since the result is in decimal number, proceed to linear
interpolation.
4. Find the difference between the two values wherein Q1 is
situated
5. Multiply the result in step 2 by the decimal part obtained in
step 4
6. Add the result in step 5 to the second smaller number in
step 4

12. QUARTILE FOR UNGROUPED DATA
Example 2.
Find the first quartile (Q1) and third quartile
(Q3), given the scores of 9 students in their
mathematics activity using linear interpolation
1, 27, 16, 7, 31, 7, 30, 3, 21

13. QUARTILE FOR UNGROUPED DATA
Step 1: Arrange the scores in ascending order
1, 3, 7, 7, 16, 21, 27, 30, 31
Step 2: Locate the position of the score in the
distribution
Q1 =
1
4
(n + 1)
=
1
4
(9 + 1)
Q1 = 2.5 th

14. QUARTILE FOR UNGROUPED DATA
Step 3:Since the result is in decimal number, proceed
to linear interpolation.
Step 4: Find the difference between the two values
wherein Q1 is situated
1, 3, 7, 7, 16, 21, 27, 30, 31
Q1 is between the values 3 and 7, therefore
= 7 – 3
= 4

15. QUARTILE FOR UNGROUPED DATA
Step 5: Multiply the result in step 2 by the decimal
part obtained in step 4
= 4( 0.5)
= 2
Step 6: Add the result in step 5 to the second smaller
number in step 4
= 3 + 2
= 5
Therefore the value of Q1 is equal to 5

16. QUARTILE FOR UNGROUPED DATA
Find the 3rd Quartile (Q3) = ?

17. QUARTILE FOR UNGROUPED DATA
Step1: 1, 3, 7, 7, 16, 21, 27, 30, 31
Step 2: Q3 =
3
4
(n + 1)
=
3
4
(9 + 1)
Q1 = 7.5 th
Step 3:
Step 4: Q3 is between 27 and 30
30 – 27 = 4
Step 5: 4(0.5) = 2
Step 6: 27 + 2 = 29

18. QUARTILE FOR UNGROUPED DATA
Activity 1
1. Find the Q1, Q2 and Q3 given the scores of 11
students in their Mathematics activity using
Mendenhall and Sincich Method
4, 9, 7, 14, 10, 8, 12, 15, 6, 11, 9
2. Find the Q1, Q2 and Q3 given the scores of 11
students in their Mathematics activity using linear
interpolation: 4, 9, 7, 14, 10, 8, 12, 15, 6, 11

19. DECILES
 Deciles are the nine score points which
divide a distribution into ten equal parts.

20. DECILES FOR UNGROUPED DATA
Example 3
Find the 3rd decile or D3 of the following scores
of a random sample of ten students:
35, 42, 40, 28, 15, 23, 33, 20, 18 and 28.

21. DECILES FOR UNGROUPED DATA
Solution:
Arrange in ascending order.
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
To find its D3 position, use the Dk =
𝑘
10
(n + 1) and
round off to the nearest integer.
D3 =
3
10
(n + 1) =
3
10
(10 + 1) =
3
10
(11) = 3.3 ≈ 3
D3 is the 3rd element
Therefore, D3 = 20

22. DECILES FOR UNGROUPED DATA
Example 4
a. Mrs Labonate gave a test to her students in
statistics. The students finished their test in 35
minutes. This time is the 2.5th decile of the allotted
time. What does this mean?
b. Anthony is a secretary in one big company in
Metro Manila. His salary is in the 7th decile. Should
Anthony be glad about his salary or not? Explain
your answer.

23. DECILES FOR UNGROUPED DATA
Explanation
a. This means that 25% of the learners finished
the test. A low quartile considered good,
because it means the students finished the test
in a short period of time.
b. 70% of the employees receive a salary that is
less than or equal to his salary and 30% of the
employees receive a salary that is greater than
his salary. Anthony should be pleased with his
salary.

24. DECILES FOR UNGROUPED DATA
Activity 2
Mrs. Marasigan is a veterinarian. One morning,
she asked her secretary to record the service
time for 15 customers. The following are
service times in minutes: 20, 35, 55, 28, 46, 32,
25, 56, 55, 28, 37, 60, 47, 52, 17. Find the
value of 2nd decile, 6th decile and 8th decile.

25. PERCENTILES
 are ninety-nine score points which divide the
distribution into one hundred equal parts, so
that each part represent the data set.

26. PERCENTILES FOR UNGROUPED DATA
Example 5
Find the 60th percentile or P60 of the following
test scores of a random sample of ten
students:
35, 42, 40, 28, 15, 23, 33, 20, 18 and 28.

27. PERCENTILES FOR UNGROUPED DATA
Solution:
Arrange in ascending order.
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
To find its P60 position, use the Dk =
𝑘
100
(n + 1)
and round off to the nearest integer.
P60 =
60
100
(n + 1) =
60
100
(10 + 1) =
60
100
(11) = 6.6 ≈
7
P60 is the 7th element
Therefore, P60 = 33

28. PERCENTILES
Activity 3
The scores of Miss World candidates from
seven judges were recorded as follows:
8.45, 9.20, 8.56, 9.13, 8.67, 8.85 and 9.17.
What is the P35 of the judges’ scores?

29. MEASURES OF POSITION FOR
GROUPED DATA