Page 124 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV Σdx
lekUrj ekè; (X ) = A +
N
26
X = 110 – = 110 – 2.6 = 107.4
10
N + 1 10 + 1
M = Size of = = 5.5th term
2 2
106 + 109 215
∴ M= = = 107.5
2 2
Σ 2 Σdx L dxO 2 2404 F G − 26I J 2
M P
−
−
σ = N N Q = 10 H 10 K
N
.
= 240 4. − 6 76 = . 233 64 = 15.285
3(X − M ) 3 107 4 − 107 5) 3X − 0 1
.
.
.
(
fo"kerk xq.kkad ;k J= = = = 0.02
.
σ 15 285 15 285
.
vr% Js.kh esa vYi&ek=kk dh Í.kkRed fo"kerk (Negative Skewness) gSA
mnkgj.k (Illustration) 2: ,d lead caVu dk fi;lZu fo"kerk xq.kkad 0.5 gS] fopj.k xq.kkad 40% gS vkSj
cgqyd 80 gSA caVu dk lekUrj ekè; rFkk eè;dk Kkr dhft,A
gy (Solution):
J = + 0.5, C.V. = 40%, Z = 80, X = ?, M = ?
X − Z X − 80
J= or 0.5 = or 0.5 σ = X – 80 or X – 0.5σ = 80 ...(i)
σ σ
σ σ
C.V. = × 100 or 40 = × 100 or 40X = 100σ or 0.4X – σ = 0 ...(ii)
X X
lehdj.k (i) dks 0.4 ls xq.kk djosQ mlesa ls lehdj.k (ii) ?kVkus ij]
0.4X – 0.2σ = 32

0.4X – 1 σ = 0
0.8 σ = 32 ∴σ = 40

leh- (ii) esa σ dk eku j[kus ij]
0.4X – 40 = 0 ∴ X = 40/0.4 = 100
3(X − M ) 300 − 3M
J= or 0.5 = or 20 = 300 – 3M
σ 40
∴ M = 93.33

mnkgj.k (Illustration) 3: oSQyh lw=k }kjk fuEu caVuksa esa leferrk dh rqyuk dhft,μ
Size : 102 104 106 108 110 112 114
Group A : 10 16 24 22 50 15 12
Group B : 15 22 55 26 18 20 3

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