The document outlines a lesson for students on measures of position, specifically focusing on quartiles and deciles as techniques for dividing a data set into equal groups. It provides explanations, examples, and calculations to find quartiles and deciles, alongside activities for students to practice their understanding. Additionally, it emphasizes the importance of arranging data in ascending order to apply these statistical concepts correctly.

2. Student

3. Prayer Before Class
[Lord, help us in our work today]
[give us concentration] [so that may we
listen,] [understand,] [learn]
[and have a peaceful mind]
[and may we always remember]
[that Jesus Christ is always with us.]
[Amen...]

4. Good Day!

5. Let’s
RECALL!

6. What are the topics
which you have already
finished this quarter?
QUARTILE
DECILE
PERCENTILE

7. Are those lessons seem
familiar to you? Why or
why not?
QUARTILE
DECILE
PERCENTILE

8. MEASURE
OF POSITION

9. MEASURES OF POSITION
-are techniques that divide
a set of data into equal
groups

10. THE DIFFERENT MEASURES
OF POSITION ARE:
• QUARTILES
• DECILES
• PERCENTILES

11. Let’s
have an activity!
No. 1

12. 4 PICS 1 WORD
M E A S U R E

13. 4 PICS 1 WORD
P O S I T I O N

14. 4 PICS 1 WORD
D I V I D E

15. 4 PICS 1 WORD
F O U R

16. 4 PICS 1 WORD
E Q U A L

17. 4 PICS 1 WORD
P A R T S

18. 4 PICS 1 WORD

19. Answer
POSITION MEASURE DIVIDED
INTO FOUR EQUAL PARTS

20. QUARTILE
POSITION MEASURE DIVIDED
INTO FOUR EQUAL PARTS
Note: the data must be
arranged in ascending order

21. QUARTILES CAN BE
APPLIED WHEN:
1. Dealing with large amount of data, which
includes the timely results for standardized
tests in school etc.
2. Trying to discover the smallest as well as the
largest values in a given distribution
3. Examining financial fields for academic as well

22. quartiles
The quartiles are the score points
which divide a distribution into four
equal parts

23. quartiles
25% 50% 75% 100%
LOWER
QUARTILE
Q1
MIDDLE QUARTILE
Q2
UPPER
QUARTILE
Q3

24. EXAMPLE:
The scores of 7 students in a
mathematics seatwork are:
7, 4, 3, 6, 7, 4, 8

25. To FIND q1, q2, and q3
7, 4, 3, 6, 7, 4, 8
Qk =
𝒌
𝟒
(𝒏 + 𝟏)
k- the quartile position
n- total number of objects or sample

26. Arrange the given data
3, 4, 4, 6, 7, 7, 8
Qk =
𝒌
𝟒
(𝒏 + 𝟏)
k- 1
n- 7
Q1 =
𝟏
𝟒
(𝟕 + 𝟏)
Q1 =
𝟏
𝟒
(𝟖)
Q1 =
𝟖
𝟒
Q1 = 2
Q1 = 4

27. q2
3, 4, 4, 6, 7, 7, 8
Qk =
𝒌
𝟒
(𝒏 + 𝟏)
k- 2
n- 7
Q2 =
𝟐
𝟒
(𝟕 + 𝟏)
Q2 =
𝟐
𝟒
(𝟖)
Q2 =
𝟏𝟔
𝟒
Q2 = 4
Q2 = 6

28. q3
3, 4, 4, 6, 7, 7, 8
Qk =
𝒌
𝟒
(𝒏 + 𝟏)
k- 3
n- 7
Q3 =
𝟑
𝟒
(𝟕 + 𝟏)
Q3 =
𝟑
𝟒
(𝟖)
Q3 =
𝟐𝟒
𝟒
Q3 = 6
Q3 = 7

29. summary
3, 4, 4, 6, 7, 7, 8
Q1 = 4
Lower quartile
25% of the
Scores is lower
than 4
Q2 = 6
Middle quartile
50% of the
Scores is lower
than 6
Q3 = 7
Upper quartile
75% of the
Scores is lower
than 7

30. Mendenhall and Sincich Method
Lower Quartile (L) = Position of
Q1 =
𝟏
𝟒
𝒏 + 𝟏
then round to the nearest integer. If L falls
halfway between two integers, round up. The
Lth element is the lower quartile value (Q1)

31. Upper Quartile (U) = Position of
Q3 =
𝟑
𝟒
𝒏 + 𝟏
then round to the nearest integer. If U falls halfway
between two integers, round down. The Uth
element is the upper quartile value (Q3)
Mendenhall and Sincich Method

32. Median = Position of
Q2 =
𝟐
𝟒
𝒏 + 𝟏 or Q2 =
𝟏
𝟐
𝒏 + 𝟏
The middle value is between the lowest value
and the largest value.
Mendenhall and Sincich Method

33. 1. Subtract the lower data from the next
data.
2. Multiply the result by the decimal
obtained in Q1.
3. Add the result in step 2, to the lower
number.
Steps of Interpolation

34. The following are test scores (out of 100) for a particular math
class.
44 56 58 62 64 64 70 72 72 72
74 74 75 78 78 79 80 82 82 84
86 87 88 90 92 95 96 96 98 100
Find the first quartile without linear
interpolation.
Measures of Position
Q1 =
𝟏
𝟒
𝒏 + 𝟏
Q1 =
𝟏
𝟒
𝟑𝟎 + 𝟏
Q1 =
𝟏
𝟒
𝟑𝟏
Q1 =
𝟑𝟏
𝟒
Q1 = 7.75
Q1 = 72

35. The following are test scores (out of 100) for a particular math
class.
44 56 58 62 64 64 70 72 72 72
74 74 75 78 78 79 80 82 82 84
86 87 88 90 92 95 96 96 98 100
Find the second quartile (exact value).
Measures of Position
Q2 =
78+79
2
= 78.5

36. The following are test scores (out of 100) for a particular math
class.
44 56 58 62 64 64 70 72 72 72
74 74 75 78 78 79 80 82 82 84
86 87 88 90 92 95 96 96 98 100
Find the third quartile with
interpolation.
Measures of Position
Q3 =
𝟑
𝟒
𝒏 + 𝟏
Q3 =
𝟑
𝟒
𝟑𝟎 + 𝟏
Q3 =
𝟑
𝟒
(𝟑𝟏)
Q3 =
𝟗𝟑
𝟒
Q3 = 23.25
Q3 = 90-88
=2(0.25)
=0.50
=88+0.50
=88.50

37. Let’s
have an
activity!
No.2

38. DECILE
POSITION MEASURE DIVIDED
INTO TEN EQUAL PARTS
Note: the data must be arranged in
ascending order
Deciles are the nine values (denoted D1, D2,…, D9) along the
scale that divide a data set into ten (approximately) equal
parts.
10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%

39. D1 D2 D3 D4 D5 D6 D7 D8 D9
1
10%
D1=10% D2=20% D3=30%
10
100
=
1
10
20
100
=
1
5
30
100
=
3
10
2
20%
3
30%
4
40%
5
50%
6
60%
7
70%
8
80%
9
90%
10
100%
D4=10% D5=50%
40
100
=
2
5
50
100
=
1
2
D6=60% D7=70% D8=80%
60
100
=
3
5
70
100
=
7
10
80
100
=
4
5
D9=90%
90
100
=
9
10

40. Finding the deciles.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Example 1: Find the deciles for the data below.
(D1)
Order the data
D1
3
1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29

41. Finding the deciles.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Example 1: Find the deciles for the data below.
(D4)
Order the data
D4
11
1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29

42. Finding the deciles.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Example 1: Find the deciles for the data below.
(D5)
Order the data
D5
1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
14

43. Finding the deciles.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Example 1: Find the deciles for the data below.
(D7)
Order the data
D7
1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
21

44. Finding the deciles.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Example 1: Find the deciles for the data below.
(D9)
Order the data
D9
1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
21

45. Finding the deciles.
35, 42, 40, 28, 15, 23, 33, 20, 18, 28
Example 1: Find the 3RD and 6th decile for the data below.

46. DECILE FOR UNGROUPED DATA
Decile (D) =
Position of Dk =
𝒌
𝟏𝟎
𝒏 + 𝟏
• The deciles are nine score-points which divide a
distribution into ten groups.
• Deciles are denoted as D1,D2,D3,…D9.
• They are computed in the same way as the
quartiles are calculated.

47. Example 1. Robert hit 9 balls at Grimsby driving
range. The recorded distances of his drives, measured
in yards, are given below. Find the 3rd decile for his
drives.
85, 125, 130, 65, 70, 75, 50, 140, 95
50, 65, 70, 75, 85, 95, 125, 130, 140
Ordered data
Practice
D3=
𝟑
𝟏𝟎
𝟗 + 𝟏
D3 =
𝟑
𝟏𝟎
𝟏𝟎
D3 =
𝟑𝟎
𝟏𝟎
= 𝟑 D3 = 𝟕𝟎

48. Example 1. Robert hit 9 balls at Grimsby driving
range. The recorded distances of his drives, measured
in yards, are given below. Find the 5th decile or median
for his drives.
85, 125, 130, 65, 70, 75, 50, 140, 95
50, 65, 70, 75, 85, 95, 125, 130, 140
Ordered data
Practice
D5=
𝟓
𝟏𝟎
𝟗 + 𝟏
D5 =
𝟓
𝟏𝟎
𝟏𝟎
D5 =
𝟓𝟎
𝟏𝟎
= 𝟓 D5 = 𝟖𝟓

49. Finding the deciles.
35, 42, 40, 28, 15, 23, 33, 20, 18, 28
Example 2: Find the 3RD decile for the data below.
Order the data
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
Dk =
𝒌
𝟏𝟎
𝒏 + 𝟏
D3 =
𝟑
𝟏𝟎
𝟏𝟎 + 𝟏
D3 =
𝟑
𝟏𝟎
𝟏𝟏
D3 =
𝟑𝟑
𝟏𝟎
D3 = 3.3
D3 = 3
D3 = 20

50. Finding the deciles.
35, 42, 40, 28, 15, 23, 33, 20, 18, 28
Example 2: Find the 6th decile for the data below.
Order the data
15, 18, 20, 23, 28, 28, 33, 35, 40, 42
Dk =
𝒌
𝟏𝟎
𝒏 + 𝟏
D6 =
𝟔
𝟏𝟎
𝟏𝟎 + 𝟏
D6 =
𝟔
𝟏𝟎
𝟏𝟏
D6 =
𝟔𝟔
𝟏𝟎
D3 = 6.6
D3 = 6
D3 = 28
round down

51. Try me!

52. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D1 for the data below.
D1=
𝟏
𝟏𝟎
𝟏𝟗 + 𝟏
D1 =
𝟏
𝟏𝟎
𝟐𝟎
D1 =
𝟐𝟎
𝟏𝟎
= 𝟐
D1 = 3

53. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D4 for the data below.
D4=
𝟒
𝟏𝟎
𝟏𝟗 + 𝟏
D4 =
𝟒
𝟏𝟎
𝟐𝟎
D4 =
𝟖𝟎
𝟏𝟎
= 𝟖
D4 = 11

54. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D5 for the data below.
D5=
𝟓
𝟏𝟎
𝟏𝟗 + 𝟏
D5 =
𝟓
𝟏𝟎
𝟐𝟎
D5 =
𝟏𝟎𝟎
𝟏𝟎
= 𝟏𝟎
D5 = 14

55. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D6 for the data below.
D6=
𝟔
𝟏𝟎
𝟏𝟗 + 𝟏
D6 =
𝟔
𝟏𝟎
𝟐𝟎
D6 =
𝟏𝟐𝟎
𝟏𝟎
= 𝟏𝟐
D6 = 20

56. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D8 for the data below.
D8=
𝟖
𝟏𝟎
𝟏𝟗 + 𝟏
D8 =
𝟖
𝟏𝟎
𝟐𝟎
D8 =
𝟏𝟔𝟎
𝟏𝟎
= 𝟏𝟔
D8 = 24

57. 1, 3, 5, 7, 9, 10, 10, 11, 11, 14, 19, 20, 20, 21, 23, 24, 25, 26, 29
Finding the DECILE.
1, 3, 9, 5, 10, 10, 11, 7, 25, 14, 11, 19, 20, 29,
23, 21, 26, 20, 24
Order the data
Example 1: Find the D1, D4, D5, D6 and D8 for the data
below.
D1=
𝟏
𝟏𝟎
𝟏𝟗 + 𝟏
D1 =
𝟏
𝟏𝟎
𝟐𝟎
D1 =
𝟐𝟎
𝟏𝟎
= 𝟐
D1 = 3
D4=
𝟒
𝟏𝟎
𝟏𝟗 + 𝟏
D4 =
𝟒
𝟏𝟎
𝟐𝟎
D4 =
𝟖𝟎
𝟏𝟎
= 𝟖
D4 = 11
D5=
𝟓
𝟏𝟎
𝟏𝟗 + 𝟏
D5 =
𝟓
𝟏𝟎
𝟐𝟎
D5 =
𝟏𝟎𝟎
𝟏𝟎
= 𝟏𝟎
D5 = 14
D6=
𝟔
𝟏𝟎
𝟏𝟗 + 𝟏
D6 =
𝟔
𝟏𝟎
𝟐𝟎
D6 =
𝟏𝟐𝟎
𝟏𝟎
= 𝟏𝟐
D6 = 20
D8=
𝟖
𝟏𝟎
𝟏𝟗 + 𝟏
D8 =
𝟖
𝟏𝟎
𝟐𝟎
D8 =
𝟏𝟔𝟎
𝟏𝟎
= 𝟏𝟔
D8 = 24

58. DECILE FOR UNGROUPED DATA
Decile (D) =
Position of Dk =
𝒌
𝟏𝟎
𝒏 + 𝟏
• The deciles are nine score-points which divide a distribution into ten groups.
• Deciles are denoted as D1,D2,D3,…D9.
• They are computed in the same way as the quartiles are calculated.
DECILE
POSITION MEASURE DIVIDED INTO TEN
EQUAL PARTS

59. Do we learn something new?

60. The owner of a coffee shop recorded the number
of costumers who come into his café each hour
in a day. The results were 14, 9, 7, 10, 12, 9, 17,
5, 8, 9, 14, 10, 11.
Find the D2, D4, D5, D7and D9 of the given problem
below. ( with interpolation)

61. Answer

62. Order the data
n=13
Using formula:
5, 7, 8, 9, 9, 9, 10, 10, 11, 12, 14, 14, 17
D2=
𝟐
𝟏𝟎
𝟏𝟑 + 𝟏
D2 =
𝟐
𝟏𝟎
𝟏𝟒
D2 =
𝟐𝟖
𝟏𝟎
= 𝟐. 𝟖
D2 = 8-7 =1 1st step
= 1(0.8) 2nd step
=0.8
=7+0.8 3rd step
D1 = 7.8
D4=
𝟒
𝟏𝟎
𝟏𝟑 + 𝟏
D4 =
𝟒
𝟏𝟎
𝟏𝟒
D4 =
𝟓𝟔
𝟏𝟎
= 𝟓. 𝟔
D4 = 9-9 =0 1st step
= 0(0.6) 2nd step
=0
=9+0 3rd step
D4 = 9

63. Order the data
n=13
Using formula:
5, 7, 8, 9, 9, 9, 10, 10, 11, 12, 14, 14, 17
D5=
𝟓
𝟏𝟎
𝟏𝟑 + 𝟏
D5 =
𝟓
𝟏𝟎
𝟏𝟒
D5 =
𝟕𝟎
𝟏𝟎
= 𝟕
D7=
𝟕
𝟏𝟎
𝟏𝟑 + 𝟏
D7 =
𝟕
𝟏𝟎
𝟏𝟒
D7 =
𝟗𝟖
𝟏𝟎
= 𝟗. 𝟖
D7 = 12-11 =1 1st step
= 1(0.8) 2nd step
=0.8
=11+0.8 3rd step
D7 = 11.8
D5 = 10
D9=
𝟗
𝟏𝟎
𝟏𝟑 + 𝟏
D9 =
𝟗
𝟏𝟎
𝟏𝟒
D9 =
𝟏𝟐𝟔
𝟏𝟎
= 𝟏𝟐. 𝟔
D9 = 17-14 =3 1st step
= 3(0.6) 2nd step
=1.8
=14+1.8 3rd step
D9 = 15.8

64. Thank You!
That’s All