Quartile deviation

2. Quartile deviation:
It is based on the lower quartile 1Q and the upper quartile 3Q . The
difference 3 1Q Q− is called the inter quartile range. The difference
3 1Q Q− divided by 2 is called semi-inter-quartile range or the quartile
deviation. Thus Quartile Deviation is
2
. 13 QQ
DQ
−
=
Coefficient of Quartile Deviation 100
13
13

+
−
=
QQ
QQ
Example-3: From the data 6, 9, 12, 14, 8, 11
(a) Find all Quartiles
(b) Find interquartile range
(c) Find quartile deviation
(d) Find coefficient of dispersion
Solution:
First arrange the data in ascending order.
6, 8, 9 , 11, 12, 14
(a)Q1 (Median of First half) = 8
Q2 (Median) = 10
2
119
=
+
Q3 (Median of 2nd
Half) = 12
(b) interquartile range = Q3 - Q1 = 12 – 8 = 4
(c) 2
2
812
2
. 13
=
−
=
−
=
QQ
DQ

3. (d)Coefficient of Quartile Deviation %20100
812
812
100
13
13
=
+
−
=
+
−
=
QQ
QQ
Example-4: From the data 6, 8, 24, 20, 15, 18, 19, 13, 11
(a) Find all Quartiles
(b) Find interquartile range
(c) Find quartile deviation
(d) Find coefficient of dispersion
Solution:
First arrange the data in ascending order.
6, 8, 11, 13, 15, 18, 19, 20, 24
(a) Q1 (Median of First Half) = 5.9
2
118
=
+
Q2 (Median) = 15
Q3 (Median of 2nd
Half) = 5.19
2
2019
=
+
(b) interquartile range = Q3 - Q1 = 19.5 – 9.5 = 10
(c) 5
2
5.95.19
2
. 13
=
−
=
−
=
QQ
DQ
(d) Coefficient of Quartile Deviation:
%48.34100
5.95.19
5.95.19
100
13
13
=
+
−
=
+
−
=
QQ
QQ

4. Example-5: Find Quartile deviation and coefficient of Quartile
deviation.
C.I f C.B c.f
2.5 – 2.9 2 2.45 – 2.95 2
3.0 – 3.4 7 2.95 – 3.45 9
3.5 – 3.9 17 3.45 – 3.95 26
4.0 – 4.4 25 3.95 – 4.45 51
4.5 – 4.9 20 4.45 – 4.95 71
5.0 – 5.4 12 4.95 – 5.45 83
5.5 – 5.9 9 5.45 – 5.95 92
6.0 – 6.4 8 5.95 – 6.45 100
∑f=100
1
100
25
4 4
3.45
3.95 3.45 0.5
For Q
f
l
h

= =
=
= − =
( )
1
1
17
. 9
.
4
0.5
3.45 25 9 3.92
17
f
c f
h f
Q l c f
f
Q
=
=
 
= + −  
= + − =

5. 3
3 3(100)
75
4 4
4.95
For Q
f
l

= =
=
5.45 4.95 0.5
12
. 71
h
f
c f
= − =
=
=
3
3
.
4
h f
Q l c f
f
 
= + −  
 3
0.5
4.95 75 71 5.12
12
Q = + − =
3 1 5.12 3.92
. 0.6
2 2
Q Q
Q D
− −
= = =
3 1
3 1
100
Q Q
Coefficient of dispersion
Q Q
−
= 
+
5.12 3.92
100
5.12 3.92
Coefficient of dispersion
−
= 
+
13.27%Coefficient of dispersion=