This document discusses measures of position, specifically quartiles, for ungrouped data. It provides examples of calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3) for various data sets by ordering the data and using the Mendehall and Sincich formula. The document also has students practice finding quartiles for different data sets, including coffee shop customers and students' ages.

2. Have you thought of comparing
your academic performance with
that of your classmates?

3. Have you wondered what score you
need subject area qualify for
honors?

4. Whenever your teacher asks your
class to form a line according to
your height, what is your position in
relation to your classmates?

10. MEASURES OF
POSITION
By: ROBENGIE M. MONERA

11. NUMERICAL DATA MAY BE
CLASSIFIED AS:
• UNGROUPED DATA
• GROUPED DATA

12. - are techniques that divide
a set of data into equal
groups.

13. The different measures of
position are:
QUARTILE,
DECILE,
PERCENTILE

14. THE QUARTILE FOR
UNGROUPED DATA
By: ROBENGIE M. MONERA

15. The are the
score points which divide a
distribution into
QUARTILES
FOUR EQUAL PARTS.
THE QUARTILE FOR UNGROUPED DATA

16. Values that divide a list of
numbers into quarters.
1st Quartile – 25% of distribution
2nd Quartile – 50% of distribution
3rd Quartile – 75% of distribution
THE QUARTILE FOR UNGROUPED DATA

17. THE QUARTILE FOR UNGROUPED DATA
Example 1. Find the average of the lower
quartile and the upper quartile of the data.
Component Quantity
Hard disk 290
monitors 370
keyboards 260
mouse 180
speakers 430

18. THE QUARTILE FOR UNGROUPED DATA
In ascending order, the data are
180, 260, 290, 370, 430
Component Quantity
Hard disk 290
monitors 370
keyboards 260
mouse 180
speakers 430

19. THE QUARTILE FOR UNGROUPED DATA
In ascending order, the data are
180, 260, 290, 370, 430
The least value of the data is 180 and the greatest value of the
data is 430.
The middle value of the data is 290.
The lower quartile is the value that is between the least value and
the middle value.
The upper quartile is the value that is between the greatest value
and the middle value.
So, the upper quartile is 370.

20. THE QUARTILE FOR UNGROUPED DATA
Example 2. The lower quartile of a data set is
the 8th data value. How many data values
are there in the data set?
The lower quartile is median data value of the lower half of the
data set.
So, there are 7 data values before and after the lower quartile. 7 +
7 + 1 = 15
So, the number of data values in the lower half is equal to
7 + 7 + 1 = 15
So, the upper half is also 15, thus 15 + 15 + 1 = 31.

21. THE QUARTILE FOR UNGROUPED DATA
So, the upper half is also 15, thus 15 + 15 + 1 = 31.
Thus, the data set contains 31 data values.
Another Solution
1
4
𝑛 + 1 = 8
n + 1 = 32
n = 31
The other solution shows Mendehall and Sincich Method

22. THE QUARTILE FOR UNGROUPED DATA
QUARTILE FORMULA
𝑄𝑘 =
𝑘
4
𝑛 + 1
Mendehall and Sincich Method
k = represents the position of quartile
n = represents the total number of data

23. THE QUARTILE FOR UNGROUPED DATA
Example 3.
The scores of 7 students in Mathematics quiz are
7, 3, 4, 6, 7, 4, 8.
𝑄𝑘 =
𝑘
4
𝑛 + 1
𝑄1 =
1
4
7 + 1
𝑄1 =
8
4
= 2
𝑄2 =
2
4
7 + 1
𝑄2 =
16
4
= 4
𝑄3 =
3
4
7 + 1
𝑄3 =
24
4
= 6

24. 25% of the
scores is lower
than 4
50% of the
scores is lower
than 6
75% of the
scores is lower
than 7
THE QUARTILE FOR UNGROUPED DATA

25. GROUP Activity
THE QUARTILE FOR UNGROUPED DATA

26. Procedure :
1.Arrange the score in increasing order.
2. Find the position of Q1, Q2 & Q3 using the
formula (Mendehall and Sincich Method)
3. Identify the value of their respective scores.
THE QUARTILE FOR UNGROUPED DATA

27. GROUP Activity:
The owner of a coffee shop recorded the
number of costumers who came into his
café each hour in a day. The results were 14,
10, 12, 9 17, 5, 8, 9, 14, 10, and 11. Find the
lower quartile and the upper quartile of the
data.
THE QUARTILE FOR UNGROUPED DATA

28. Guide Questions:
the data in ascending order
5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17
1. What is Q1, Q2, and Q3 of their scores?
2. How many students belong to Q1, Q2, Q3 in
of their scores?
3. Have you realize of finding the position of the
scores?
THE QUARTILE FOR UNGROUPED DATA

29. THE QUARTILE FOR UNGROUPED DATA
Where do we apply the
measure of position?
Generalization:

30. THE QUARTILE FOR UNGROUPED DATA
Evaluation:
Get 1/2 sheet of intermediate
paper and answer the given data.

31. Students Name Age
ANNA 10
TONY 11
DENNIS 12
AIRA 13
ANTONETTE 13
CHRISTIAN 13
SUSAN 14
LITO 14
MICHAEL 15
GLADYS 15
1. WHAT IS Q1, Q2, Q3 OF
THEIR AGES?
2.HOW MANY STUDENTS
BELONG TO Q1, Q2, Q3 IN
TERMS OF THEIR AGES?
THE QUARTILE FOR UNGROUPED DATA

32. THE QUARTILE FOR UNGROUPED DATA
Assignment:
Answer Activity 8 “Aqua
Running” on page 372.
Write your answer in your activity
notebook

33. THE QUARTILE FOR UNGROUPED DATA
Thank you