Measures of Location Measures of Location Dr. Romario Bhong P. YbaezResearch DirectorSt. Paul University Dumaguete

MEASURES OF LOCATION MEASURES OF LOCATION (FRACTILES)(FRACTILES)1. Quartiles (Qi)

(i /4)(n) values of the ordered set liesbelow Qi.below Qi.

One-fourth or 25% < Q1. Half or 50% < Q2 (Q2= Md) Three-fourths or 75% < Q3

Example 1. 2 4 6 8 Q1 Q2 Q3

32

42Q

itbelowlies1)4(4

1for which :

i

1

valuesvaluesQ

72

86Q

itbelowlie values3)4(4

3for which value:Q

52

64Q

itbelowlies values2)4(4

2for which :

2

3

3

2

2

i

valueQ

2. 3 5 7 9 12 Q1 Q2 Q3

42

8

2

53Q

itbelowlies1.25)5(4

1for which :

i

1

valuesvaluesQ

82

97Q

itbelowlie values.753)5(4

3for which value:Q

7Q

itbelowlies values5.2)5(4

2for which :

22

3

3

2

2

valueQ

2. Deciles (Di) (i/10)(n) values of the ordered set lies below Di. One-tenth or 10% < D1. Two-tenths or 20% < D2. In general, (i x 10)% of the data values are less

Di D = Md D5 = Md Example. Given the following scores 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

Solution:

9108

Dit;belowlie values45.4)15(3

:

72

86D;it belowlie values3)15(

10

2:

32

42Dit;belowlie value15.1)15(

10

1:

33

22

11

D

D

D

15D;it belowlievalues5.7)15(10

5:

132

1412Dit;belowlie values6)15(

10

4:

92

Dit;belowlie values45.4)15(10

:

55

44

33

D

D

D

25Dit;belowlievalues12)15(8

:

21Dit;belowlievalues105.10)15(10

7:

19Dit;belowlievalues9)15(10

6:

77

66

D

D

D

27Dit;belowlievalues5.13)15(10

9:

25Dit;belowlievalues12)15(10

8:

99

88

D

D

3. Percentile (Pi) (i/100)(n) values of the ordered set lies below

Pi. One per cent < P1. Two per cent < P2. P =Md=Q ; P = Q ; P = Q P50=Md=Q2; P25 = Q1; P75 = Q3 In general, i % < Pi.Example. Given the following scores: 80, 92,

85, 87, 94, 83, 88, 91, 92, and 80. Array: 80, 80, 83, 85, 87, 88, 91, 92, 92, 94

Solution:P25: 25%(10)=2.5; P25 =(80+83)/2 =81.5P50: 50%(10) = 5;P50 =(87+88)/2= 87.5P60: 60%(10) = 6; P60 = (88+91)/2=89.5P75:75%(10)=7.5; P75=(91+92)/2= 91.5