Consists solved numerical problems on Quartile Deviation step by step along with answers. It covers whole three series of Individual, Discrete and Continuous series. Unsolved numerical problems are also there for practice.

1. Quartile Deviation
Individual Series
1. 24,7,11,9,17,3,20,14,4,22,27.
Arranging series in ascending order,
3,4,7,9,11,14,17,20,22,24,27.
N= 11
Q1 = (N+1)th item
4
Q1 = (11+1)th item
4
Q1 = 12/4th item
Q1 = 3rd
item
Q1 = 7
Q3 = 3(N+1)th item
4
Q3 = 3(11+1)th item
4
Q3 = 36th item
4
Q3= 9th
item
Q3 = 22
Q.D.= Q3 – Q1
2
Q.D. = 22-7
2
Q.D. = 15/2
Q.D.= 7.5
Coefficient of Q.D.
= Q3 – Q1
Q3 + Q1
= 22-7
22+7
= 15/19 = 0.52

2. Do it yourself:
1. 19,9,15,21,4,3,23,11,7,26,14. (Ans.14,7 and 0.5)
2. 20,28,12,40,50,15,30. (Ans. 25,12.5 & 0.455)
Discrete Series
1.
x f cf
4 4 4
8 9 13
12 17 30
16 40 70
20 53 123
24 37 160
28 24 184
32 16 200
N=
200
Q1 = (N+1)th item
4
Q1 = (200+1)th item
4
Q1 = 201/4th item
Q1 = 50.25th item
Q1 = 16
Q3 = 3(N+1)th item
4
Q3 = 3(200+1)th item
4
Q3 = 603th item
4
Q3= 150.75th item
Q3 = 24
Q.D.= Q3 – Q1
2
Q.D. = 24-16
2
Q.D. = 8/2

3. Q.D.= 4
Coefficient of Q.D.
= Q3 – Q1
Q3 + Q1
= 24-16
24+16
= 8/40 = 0.20
Do it yourself:
1.
X 50 51 52 53 54 55 56
f 10 12 15 10 14 18 6
(Ans.0.038)
2.
X 10 20 30 40 50 60
f 4 7 15 8 7 2
(Ans. 20,10, 0.333)
Continuous Series
C.I. f c.f.
0-10 8 8
10-20 16 24
20-30 22 46
30-40 30 76
40-50 24 100
50-60 12 112
60-70 6 118
N=118
Q1= L+ N1-cf X i
f
N= 118
N1 = N/4
118/4= 29.5
cf= 24
f=22

4. i= 10
L= 20
Q1= 20 + 29.5-24 X 10
22
Q1= 20+ 5.5 X 10
22
Q1= 20+ 2.5
Q1= 22.5 Ans.
Q3= L+ N1-cf X i
f
N= 118
N1 = 3(N/4)
3(118/4)= 88.5
cf= 76
f=24
i= 10
L= 40
Q3= 40 + 88.5-76 X 10
24
Q3= 20+ 12.5 X 10
24
Q3= 40+ 5.20
Q3= 45.20 Ans.
Q.D.= Q3 – Q1
2
Q.D. = 45.20-22.5
2
Q.D. = 22.7/2
Q.D.= 11.35
Coefficient of Q.D.
= Q3 – Q1
Q3 + Q1

5. = 45.20-22.5
45.20+22.5
= 22.7/67.7 = 0.335
Do it yourself:
1.
C.I. 50-53 53-56 56-59 59-62 62-65 65-68
f
2 7 24 27 13 3
(Ans.2.21, 0.037)
2.
X 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
f
11 37 88 138 92 63 36 15
(Ans.38.18,59.35,0.217)
3.
x 0-10 10-30 30-70 70-120 120-150 150-180 180-200
f
6 17 34 58 44 30 17
(Ans.63.53,146.43,41.7,0.39)
E-notes by:
Asst. Prof. Harpreet Kaur