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Question

Find the mean deviation from the mean for the following data:
(i)
xi 5 7 9 10 12 15
fi 8 6 2 2 2 6

(ii)
xi 5 10 15 20 25
fi 7 4 6 3 5

(iii)
xi 10 30 50 70 90
fi 4 24 28 16 8

(iv)
Size 20 21 22 23 24
Frequency 6 4 5 1 4
                                                                                      
                                                                                       [NCERT EXEMPLAR]
(v)
Size 1 3 5 7 9 11 13 15
Frequency 3 3 4 14 7 4 3 4
                                                                                      
                                                                                       [NCERT EXEMPLAR]


Solution

i)
xi fi fixi
xi-x¯
fixi-9
5 8 40 4 32
7 6 42 2 12
9 2 18 0 0
10 2 20 1 2
12 2 24 3 6
15 6 90 6 36
  N=Σfi=26 i=1nfixi = 234   i=1nfixi-9=88
x=fii=1nxiN=23426=9
M.D.=1Ni=1nfixi-x=126×88=3.39


ii)
xi fi fixi xi-x¯ fixi-14
5 7 35 9 63
10 4 40 4 16
15 6 90 1 6
20 3 60 6 18
25 5 125 11 55
  N=25 i=1nfixi=350   i=1nfixi-14=158
x=fii=1nxiN=35025=14
MD=1Ni=1nfixi-x=125×158=6.32


iii)
xi fi fi​xi xi-x¯ fixi-50
10 4 40 40 160
30 24 720 20 480
50 28 1400 0 0
70 16 1120 20 320
90 8 720 40 320
  N=80 i=1nfixi=4000   i=1nfixi-50=1280
x=fii=1nxiN=400080=50
MD=1Ni=1nfixi-x=180×1280=16

(iv)
Size(xi) Frequency (fi) fi​xi xi-x¯=xi-21.65 fixi-x=fixi-21.65
20 6 120 1.65 9.9
21 4 84 0.65 2.6
22 5 110 0.35 1.75
23 1 23 1.35 1.35
24 4 96 2.35 9.4
  N=20 i=1nfixi=433   i=1nfixi-x=25
x=fii=1nxiN=43320=21.65
MD=1Ni=1nfixi-x=120×25=1.25

(v)
Size(xi) Frequency (fi) fi​xi xi-x¯=xi-8 fixi-x=fixi-8
1 3 3 7 21
3 3 9 5 15
5 4 20 3 12
7 14 98 1 14
9 7 63 1 7
11 4 44 3 12
13 3 39 5 15
15 4 60 7 28
  N=42 i=1nfixi=336   i=1nfixi-x=124
x=fii=1nxiN=33642=8
MD=1Ni=1nfixi-x=142×124=2.95

Mathematics
RD Sharma XI (2019)
All

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