This document discusses various measures of position for ungrouped data including quartiles, deciles, and percentiles. It provides definitions and formulas for calculating these measures, and works through examples finding the quartiles, deciles, and percentiles for sample data sets.

2. M E
E A S U R

3. T N
P O S I I O

4. D V
I I D E

5. F O U R

6. T E N

7. U E D
H N D R

8. E Q U A L

9. P T
A R S

11. Measures of Position
for Ungrouped Data
-are techniques that divides a
set of data into equal groups.
-include not only central
location but also any position
depending on the number of
equal divisions in a given
distribution.

12. *QUARTILES
*DECILES
*PERCENTILES

13. - are the scorepoints
which divide a
distribution into four
equal part.

14. LOWER
QUARTILE
MIDDLE
QUARTILE
UPPER
QUARTILE

15. Position of Qk =
𝒌
4
(𝑛 + 1)
where,
k = quartile position (1, 2, 3)
n = total number of cases

16. *Arrange the data from lowest to
highest (ascending) order.
* Round off the value to the nearest
integer.
* If lower quartile falls halfway
between two integers, round up.
* If upper quartile falls halfway
between two integers, round down.

17. The difference between the
upper quartile 𝑄3 and the lower
quartile 𝑄1 in a set of data is the
interquartile range.
Interquartile Range= 𝑄3 − 𝑄1

18. The scores of seven
student in a Mathematics
seatwork are:
7, 4, 3, 6, 7, 4, 8.
Find Q1,Q2,Q3.
Find the interquartile range.

19. Qk =
𝒌
4
(𝑛 + 1)
3 4 4 6 7 7 8
To find Q1,Q2, and Q3

20. 3 4 4 6 7 7 8
LOWER
QUARTILE
MIDDLE
QUARTILE
UPPER
QUARTILE
25% of the
scores is
lower than 4
50% of the
scores is
lower than 6
75% of the
scores is
lower than 7

21. A group of students obtained
the following scores in their
statistics quiz:
27, 1, 16, 7, 7, 21, 3, 30, and 31.
Find the upper quartile and lower
quartile.

22. 1 3 7 7 16 21 27 30 31
Position of Q1 =
1
4
(𝑛 + 1)
=
1
4
(9 + 1)
=
1
4
(10)
= 𝟐. 𝟓
The computed value 2.5 becomes 3
after rounding up. The lower quartile
value is the 3rd element, so Q1 = 7
Q1

23. 1 3 7 7 16 21 27 30 31
Position of Q3 =
3
4
(𝑛 + 1)
=
3
4
(9 + 1)
=
3
4
(10)
= 𝟕. 𝟓
The computed value 7.5 becomes 7 after
rounding down. The upper quartile value
is the 7th element, so Q3 = 27
Q1 Q3

24. - are the nine score points
which divide a distribution
into 10 equal parts. Denoted
as D1, D2, D3,…,D9.
-they are computed in the
same way that the quartiles
are calculated.

25. Position of Dk =
𝒌
10
(𝑛 + 1)
where,
k = decile position (1, 2, 3,…,9)
n = total number of cases

26. A group of students
obtained the following scores in
their statistics quiz:
27, 1, 16, 7, 7, 21, 3, 30, and
31.
Find the 3rd decile.

27. 1 3 7 7 16 21 27 30 31
Position of D3 =
3
10
(𝑛 + 1)
=
3
10
(9 + 1)
=
3
10
(10)
= 𝟑
The 3rd decile value is in the 3rd
element, so D3 = 7
D3

28. - are the ninety-nine score
points which divide a
distribution into 100 equal
parts. Denoted as P1, P2,
P3,…,P99.

29. Position of Pk =
𝒌(𝑛+1)
100
where,
k = percentile position (1, 2, 3,…,99)
n = total number of cases

31. A group of students
obtained the following scores in
their statistics quiz:
27, 1, 16, 7, 7, 21, 3, 30, and
31.
Find the 70th percentile.

32. 1 3 7 7 16 21 27 30 31
Position of P70 =
70
100
(𝑛 + 1)
=
70
100
(9 + 1)
=
70
100
(10)
= 𝟕
The 70th percentile value is in the 7th
element, so P70 = 27.
P3

33. *If we are dealing a large
amount of data.
*If we are trying to discover
the smallest as well as the
largest values in a given
distribution.

34. 1
2
3
4
5

35. Group 1
Find the 3rd decile and P30 of the
following test scores of a random sample
of ten students:
35, 42, 40, 28, 15, 23, 20, 18, and 28.

36. 15 18 20 23 28 28 35 40 42
Position of D3=
3
10
(𝑛 + 1)
=
3
10
(9 + 1)
=
3
10
(10)
= 3
The value of 3rd decile is in 3rd
element, so D3 = 20
D3
No need to solve for P30 because the
position of P30 is the same as D3

37. Group 2
The scores of Miss World
candidates from the seven judges
were recorded as follows:
8.45, 9.20, 8.56, 9.13, 8.67, 8.85
and 9.17
Find the 35th percentile or 𝑃35
and𝑄1 of the judges’ scores?

38. Group 3
Shopping Time
Time People
2 450
4 1500
6 2300
8 5700
10 6850
12 8000
A total of 8000 people
visited a shopping mall
over 12 hours.
Find the third quartile.
Find the 40th percentile.

39. Complete the Cross Quantile Puzzle by finding the specified
measures of position. Use Mendenhall Method. (In filling the
boxes, disregard the decimal point. For example, 14.3
should be written as
Given: Scores 5, 7, 12, 14, 15, 22, 25, 30,
36, 42, 53, 65
Across
2. D7
4.
65(𝑛+1)
100
8.
90(𝑛+1)
100
9. P9
Down
1. Q2
3.
90(𝑛+1)
100
5. P40
6. P52
7. P54
1 4 3
1 2 3
4
5 6
7 8
9

40. ASSIGNMENT:
The following are the number of hours
worked in a week by 10 employees of Santiago
Law Firm.
Earl – 42 Joeven – 34
Nelson – 48 George – 39
John – 50 Brix– 40
Mark – 21 Von – 57
William – 23 Louie – 38
Among the employees, whose number of
hours corresponds to the first quartile? P75? 5th
decile?