This document defines measures of position such as quartiles, deciles, and percentiles. It explains that these are techniques used to divide ordered data into equal groups in order to describe the position of data values relative to the rest of the data set. Quartiles specifically divide a data set into four equal parts, with the first quartile (Q1) separating the lowest 25% of values, the second quartile (Q2) or median separating the middle 50% of values, and the third quartile (Q3) separating the highest 25% of values. The document provides examples of calculating quartiles for ungrouped data sets.

1. MEASURES OF
POSITION
F O U R T H Q U A R T E R - S T A T I S T I C S

2. OBJECTIVES
•Define measures of position
•Illustrate the following measures of
position:
–Quartiles
–Deciles
–Percentiles

3. NUMERICAL INFORMATION MAY BE
CLASSIFIED AS:
•Ungrouped data
•Grouped data

5. MEASURES OF POSITION/QUANTILES
- are techniques that divide a
set of data into equal groups
Fractiles are numbers that partition or
divide an ordered data set into equal parts.

6. MEASURES OF POSITION/QUANTILES
•Used to describe the position
of a data value in relation to
the rest of the data.
Types:
1. Quartiles
2. Percentiles
3. Deciles

7. QUANTILES CAN BE APPLIED WHEN:
•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.

8. MEASURES OF
POSITION FOR
UNGROUPED DATA
Q U A R T I L E , D E C I L E A N D P E R C E N T I L E

9. QUARTILE
U N G R O U P E D D A T A B Y I N S P E C T I O N

10. QUARTILE FOR UNGROUPED DATA
•The quartiles are the score points
which divide a distribution into
four equal parts.

11. Quartiles

12. Q1, Q2, Q3
Quartiles

13. Q1, Q2, Q3
divides ranked scores into four equal parts
Quartiles

14. Q1, Q2, Q3
divides ranked scores into four equal parts
Quartiles
25% 25% 25% 25%
Q1 Q2 Q3

15. Q1 – LOWER QUARTILE
At most,25% of data is smaller than
Q1.
It divides the lower half of a data
set in half.

16. Q2 – MIDDLE QUARTILE
•The median divides the data set in
half.
•50% of the data values fall below
the median and 50% fall above.

17. Q3 – UPPER QUARTILE
•At most,25% of data is larger than
Q3.
•It divides the upper half of the
data set in half.

18. Q1 Q2 Q3
25% 25% 25% 25%

19. EXAMPLE……
A group of students obtained the
following scores in their statistics
quiz:
8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9
(LM Activity 4,#2)

20. First,arrange the scores in ascending order:
1, 2, 3
3, 4, 5, 5
5, 6, 7, 8
8, 8, 9
Q1
Lower
Quartile
Q2
Middle
Quartile
Q3
Upper
Quartile
Observe how the lower quartile (Q1), middle quartile
(Q 2),and upper quartile (Q3) of the scores are
obtained.Complete the statements below:
The first quartile 3 is obtained by .
(observe the position of 3 from 1 to 5).
The second quartile 5 is obtained by .
(observe the position of 5 from 1 to 9).
The third quartile 8 is obtained by .
(observe the position of 8 from 6 to 9).
Middle Quartile
is also the
MEDIAN

21. EXAMPLE……
The scores of 10 students in a
Mathematics seatwork are:
7, 4, 8, 9, 3, 6, 7, 4, 5, 8
(LM Activity 4,#3)

22. First,arrange the scores in ascending order:
3 , 4 , 4 , 5 , 6 , 7 , 7 , 8 , 8 , 9
Q1
Lower
Quartile
Q2
𝟐
𝟔+𝟕
= 6.5
Q3
Upper
Quartile
Discuss with your group mates:
a. Your observations about the quartile.
b. How each value was obtained.
c. Your generalizations regarding your observations.

23. EXAMPLE……
1.The owner of a coffee shop recorded the
number of customers who came into his
café each hour in a day.The results were 14,
10,12,9 17,5,8,9 10 ,and 11.Find the
lower quartiles and upper quartile of the
data.
2.Find Q1, Q 2,and Q3.
12 ,9 ,24 ,3 ,13 ,20 ,17 ,11

24. QUARTILE
U N G R O U P E D D A T A B Y M E N D E N H A L L
A N D S I N C I C H M E T H O D