The document discusses calculating quartile deviation and the coefficient of quartile deviation from a data set. Quartile deviation is calculated as the difference between the third (Q3) and first (Q1) quartiles divided by 2. The coefficient of quartile deviation is the quartile deviation expressed as a percentage of the interquartile range. Several examples are provided to demonstrate finding the quartiles, interquartile range, quartile deviation, and coefficient of quartile deviation for data sets.

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=