Post on 10-Sep-2015
description
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