Includes solved numerical problems of Mean deviation. It has also some unsolved practical problems for practice. The file covers all three series i..e. Individual, discrete and continuous series.

1. Mean Deviation
Individual Series
1. 18,22,3,12,15,7,14.
X Dy= IX- x
̄ I
18 5
22 9
3 10
12 1
15 2
7 6
14 1
∑X = 91 ∑dy= 34
x
̄ = ∑X
N
x
̄ = 91/7 = 13
M.D. from Mean,
M.D. = ∑dy
N
M.D. = 34/7= 4.86
Coefficient of M.D.
= M.D. from Mean
Mean
= 4.86/13
= 0.37
Mean deviation from Median
3,7,12,14,15,18,22.
N=7
M= N+1 = 7+1 = 8/2= 4th
term
2 2
M= 14
X Dy= IX- MI
3 3-14=11

2. 7 7-14=7
12 12-14=2
14 14-14=0
15 15-14=1
18 18-14=4
22 22-14=8
∑dy= 33
M.D. = ∑dy
N
M.D.= 33/7 = 4.71
Coefficient of M.D. from Median
M.D. from Median
Median
= 4.71/14
= 0.336
Do it yourself:
Find M.D. and its coefficient from Mean and Median
1. 6,26,32,30,10,25. (Ans. 9.33,0.424,8,0.296)
2. 7,4,10,9,15,12,7,9,7. (Ans. 2.34,0.263,2.33,0.259)
Discrete Series
X f fx dy= IX- x
̄ I fdy
5 3 15 13.06 39.18
10 4 40 8.06 32.24
15 8 120 3.06 24.48
20 12 240 1.94 23.28
25 7 175 6.94 48.58
30 2 60 11.94 23.88
N=36 ∑fx= 650 ∑fdy= 191.64
x
̄ = ∑fx = 650/36 = 18.06
N
M.D. from Mean= ∑fdy
N
= 191.64/36

3. = 5.323
Coefficient of M.D. from Mean
M.D. = 5.323/18.06= 0.295
x
̄
x f cf IX-MI= dy fdy
5 3 3 15 45
10 4 7 10 40
15 8 15 5 40
20 12 27 0 0
25 7 34 5 35
30 2 36 10 20
N=36 ∑fdy= 180
M= N+1 = 36+1 = 37/2= 18.5
2 2
M= 20
M.D. from M= ∑fdy
N
= 180/36
= 5
Coefficient of M.D. from Median
M.D. = 5/20= 0.25
M
Do it yourself:
1. Calculate Coefficient of M.D. from Median:
X 10 20 30 40 50 60 70 80
f 3 8 16 26 37 50 56 60
(Ans. 16.3)
2. Calculate M.D. and its coefficient from Mean and Median:
X 5 10 15 20 25 30 35 40
f 16 32 36 44 28 18 12 14
(Ans. 7.66, 0.38, 7.7, 0.38)

4. Continuous Series
C.I. f m fm dy=IX- x
̄ I fdy
0-10 6 5 30 17.9 107.4
10-20 28 15 420 7.9 221.2
20-30 51 25 1275 2.1 107.1
30-40 11 35 385 12.1 133.1
40-50 4 45 180 22.1 88.4
N=100 ∑fm=2290 ∑fdy=657.2
x
̄ = ∑fm = 2290/100 = 22.9
N
M.D. from Mean= ∑fdy
N
= 657.2/100
= 6.572
Coefficient of M.D. from Mean
M.D. = 6.572/22.9= 0.28
x
̄
C.I. f cf dy=IX-MI fdy
0-10 6 6 18.14 108.89
10-20 28 34 8.14 227.92
20-30 51 85 1.86 94.86
30-40 11 96 11.86 130.46
40-50 4 100 21.86 87.44
N=100 ∑fdy=649.52
M= M= L+ N1-cf X i
F
N= 100
N1 = N/2
100/2= 50
Cf= 34
F=51
i= 10

5. l= 20
M= 20 + 50-34 X 10
51
M= 20 + 3.14
M= 23.14
M.D. from Median= ∑fdy
N
= 649.52/100
= 6.49
Coefficient of M.D. from Median
M.D. = 6.49/23.14= 0.28
M
Do it yourself:
1. calculate M.D. from median and its coefficient:
C.I. 20-30 30-40 40-50 50-60 60-70
f 8 12 20 16 4
(Ans. 8.67, 0.192)
2. compute M.D and its coefficient from Mean and Median:
C.I. 100-120 120-140 140-160 160-180 180-200
f 4 6 8 10 5
(Ans. 20.9,0.14,20.03,0.13)
E-notes by:
Asst. Prof. Harpreet Kaur