Fractiles (quantiles)

Fractiles (quantiles)

2. Fractiles (Quantiles)
There are three other measure of location quartiles, deciles and
percentiles that locate the position of certain noncentral pieces of data
relative to the entire set of data.


Example-50:
From the following data find
i) �
1,�
3
ii) ??????
3,??????
7
iii) �
30,�
90

1.8 2.9 3.4
1.9 3.0 3.5
2.2 3.1 3.6
2.5 3.2 3.9
2.6 3.3 4.1

Solution:
First arrange the data in assending order, where �=15

For �
1=25% �� �=
25
100
×15=3.75≅4�ℎ �????????????��

�
�=�.�

For �
3=75% �� �=
75
100
×15=11.25≃12�ℎ �????????????��

�
�=�.�

For ??????
3=30% �� �=
30
100
×15=4.5≃5�ℎ �????????????��

??????
�=�.�

3. For ??????
7=70% �� �=
70
100
×15=10.5≃11�ℎ �????????????��

??????
�=�.�

For �
30=30% �� �=
30
100
×15=4.5≃5�ℎ �????????????��

�
��=�.�

For �
90=90% �� �=
90
100
×15=13.5≃14�ℎ �????????????��

�
??????�=�.??????


Example-51:
Find �
1 and ??????
5 from the following data

1.8 3.0 4.1
1.9 3.2 4.2
2.5 3.4 4.5
2.6 3.7 4.7

Solution:

For �
1=25% �� �=
25
100
×12=3

We seek the value below 3 observation fall

�
1=
2.5+2.6
2


�
�=�.��

4. For ??????
5=50% �� �=
50
100
×12=6

We seek the value below 6 observation fall

??????
5=
3.2+3.4
2


??????
�=�.�