Topic: Measures of Position

1. COT 2 DEMONSTRATION
TEACHING
Presented by: Argie C. de Los Reyes

2. PRAYER

3. 4 PICS 1 WORD

4. 4 PICS 1 WORD
M
E S A
U R E

5. 4 PICS 1 WORD
S I O P I N T O

6. WHAT IS OUR
TOPIC TODAY?

7. MEASURES OF
POSITION

8. OBJECTIVES
a. define measure of position in their
own words;
b. interpret measures of position;
c. calculate the specified measures of
position; and
d. solve problems involving measures of
position for ungrouped data with
accuracy.

9. CONTEST
Follow the directions and do it as fast as
you can

10. GIVEN
A group of students obtained the
following scores in their Statistics quiz:
8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9

11. GIVEN
A group of students
obtained the
following scores in
their Statistics quiz:
8, 2, 5, 4, 8, 5, 7, 1, 3,
6, 9
PROCEDURE:
1. Arrange the scores in
INCREASING or DECREASING
order
2. Identify the lowest score and
highest score
3. Find the middle score. Label it as
𝑄2
4. Identify the value between the
middle score and the lowest
score. Label it as 𝑄1.
5. Identify the value between the
middle score and the highest
(ANSWERS)
1) 1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9
2) Lowest score = 1, highest score
= 9
3) Q2= 5
4) Q1= 3
5) Q3= 8
QUESTIONS
1) What is 𝑄1, 𝑄2, and
𝑄3 of their scores?
2) How many
students belong to
𝑄1, 𝑄2, and 𝑄3 in
terms of their
scores?
3) Have you realized
of finding the
position of the
scores?
2 students 5 students 8 students

12. DEFINITION OF MEASURES OF POSITION

13. DEFINITION OF MEASURES OF POSITION
Let’s arrange
Major Historical
Events of the
Philippines

14. DEFINITION OF MEASURES OF POSITION
INSTRUCTION:
Arrange the Major Historical Events
of the Philippines from the year 1521
to 1946 in chronological order. Use
the sticky notes and fasten them on
the board.

15. DEFINITION OF MEASURES OF POSITION
 Measures of position are techniques that divide a set of data
into equal groups.
 Numerical information may be classified as: ungrouped and
grouped data.
 To determine the measurement of position, the data must be
sorted from lowest to highest or highest to lowest.
 The different measures of position are: Quartiles, Deciles
and Percentiles.
 Measures of position are techniques that divide a set of data
into equal groups.
 Numerical information may be classified as: ungrouped and
grouped data.
 To determine the measurement of position, the data must be
sorted from lowest to highest or highest to lowest.
 The different measures of position are: Quartiles, Deciles
and Percentiles.

16. IMPORTANCE OF MEASURES OF POSITION
 Dealing with large amount of data, which includes
the timely results for standardized tests in schools,
etc.
 Trying to discover the smallest as well as the largest
values in a given distribution.
 Examining financial fields for academic as well as
statistical studies.

17. DEFINE
QUARTILE

18. DEFINE
QUARTILE
 Quartiles are the score points
which divide a distribution into
four equal parts.
 25% of the distribution are below
the first quartile (𝑄1).
 50% of the distribution are below
the second quartile (𝑄2).
 75% of the distribution are below
the third quartile (𝑄3).

19. DEFINE
QUARTILE
Formula:
𝐐𝐤 =
𝐤
𝟒
(𝐧 + 𝟏)
 First quartile: Q1 =
1
4
(n + 1)
 Second quartile: Q2 =
2
4
(n + 1)
 Third quartile: Q3 =
3
4
(n + 1)

20. DEFINE
QUARTILE
Use interpolation if 𝑸𝒌 is decimal:
a. Get the difference between
the values where 𝑄𝑘 is
located.
b. Multiply the difference
obtained in Step 1 by the
decimal part of 𝑄𝑘.
c. Add the result in Step 2, to
the 2nd or smaller number.

21. QUARTILE
a. Find lower 𝑄1, 𝑄2, and 𝑄3.
b. Interpret the results.
Ex. 1) The scores of 7
students in a
Mathematics
seatwork are:
7, 4, 3, 6, 7, 4, 8

22. QUARTILE
Solution:
 𝑄1 =
1
4
(6 + 1) =
1
4
(7) =
𝟏. 𝟕𝟓 position
 Using interpolation:
(0.75 × 1) + 2 = 0.75 + 2 = 𝟐. 𝟕𝟓
is the Q1 value
Ex. 2) Find the 𝑄1 of
the scores:
2, 3, 3, 5, 6, 9

23. SUMMARY
A. Can we apply measure of
position to
1. Determining whether a score is
high or low.
2. etermining the passing mark in a
test.
3. Finding the highest score or lowest
score in an exam.
4. Finding the arrangement of the
scores.
5. Finding the variation of scores in a
test.

24. SUMMARY
B. Arrange the following steps in
finding the measure of position for
quartile.
a) Identify the value between the
middle score and the highest
score. Label it as 𝑄3.
b) Identify the lowest score and
highest score
c) Arrange the scores in INCREASING
or DECREASING order
d) Find the middle score. Label it as 𝑄
2
e) Identify the value between the

25. LET’S APPLY YOUR KNOWLEDGE
Find the first quartile (𝑄1), second quartile (𝑄2),
and the third quartile (𝑄3), given the scores of
10 students in their Mathematics.
4 9 7 14 10
8 12 15 6 11

26. LET’S APPLY YOUR KNOWLEDGE
Find the first quartile (𝑄1), second quartile (𝑄2),
and the third quartile (𝑄3), given the scores of
10 students in their Mathematics.
4, 6, 7, 8, 9, 10, 11, 12, 14, 15

27. LET’S EVALUATE YOUR KNOWLEDGE
Alvin has an assignment to
ask at random 10 students
in their school about their
ages. The data are given in
the table on the right.
1. What is 𝑄1, 𝑄2, and 𝑄3 of their ages?
2. How many students belong to 𝑄1, 𝑄2, and 𝑄3 in terms of their
ages?

28. ASSIGNMENT
Answer Activity 8 “Aqua Running” pg. 372
(to be written on one whole sheet of paper)

29. THANK YOU!