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vFkZ'kkL=k esa lkaf[;dh; fof/;k¡
uksV (4) lekUrj ekè; ls fy, x;s fopyuksa dk oxZ gh izlj.k dgykrk gSA
izeki fopyu xq.kkadμnks Jsf.k;ksa osQ vifdj.k dh rqyuk djus osQ fy, izeki fopyu dk lkis{k eku Kkr
djrs gSa ftls izeki fopyu xq.kkad dgrs gSaA bls Kkr djus osQ fy, izeki fopyu (σ) dks lekUrj ekè; (X)
ls Hkkx ns nsrs gSa vFkkZr~
σ
izeki fopyu xq.kkad =
X
7-6 izeki fopyu osQ ifjdyu dh jhfr;k¡ (Methods of Calculation of Standard
Deviation)
O;fDrxr Js.kh (Individual Series) esa izeki fopyuμbl Js.kh esa izeki fopyu Kkr djus dh fuEu rhu
jhfr;k¡ gSaμ
(1) izR;{k jhfr] (2) ewY; oxZ jhfr] (3) y?kq jhfrA
1. izR;{k jhfr (Direct Method)μbl jhfr dh fØ;kfof/ fuEu gSμ
(a) loZizFke Js.kh dk lekUrj ekè; (X) Kkr djrs gSaA
(b) fiQj izR;sd in&ewY; esa ls lekUrj ekè; ?kVkdj fopyu Kkr dj ysrs gSaA d = (X – X )
2
(c) lHkh fopyuksa osQ oxks± dk ;ksx Σd Kkr dj ysrs gSaA
(d) fopyu oxks± osQ ;ksx dks inksa dh la[;k ls Hkkx ns nsrs gSaA ;g la[;k ;k eku f}rh; vifdj.k ?kkr ;k
izlj.k gksrh gSA
∑ d 2 ∑ X 2 ∑ −(X X ) 2
izlj.k = or = or
N N N
2. izeki fopyu Kkr djus osQ fy, bldk oxZewy Kkr djrs gSa vFkkZr~
(e) izeki fopyu Kkr djus osQ fy, bldk oxZewy Kkr djrs gSa vFkkZr~
∑ d 2 ∑ ( − X X) 2
izeki fopyu σ = =
N N
tc lekUrj ekè; iw.kk±d esa gks rc ;g jhfr mi;qDr gksrh gSA
2. ewY; oxZ jhfr (Squares-Value Method)μbl jhfr esa izeki fopyu Kkr djus osQ fy, in&ewY;ksa (X)
dk iz;ksx fd;k tkrk gS vkSj fopyu ugha fy;s tkrs gSaA bldh fuEu izfØ;k gSμ
(a) loZizFke lHkh ewY;ksa (X) dk ;ksx (∑X) Kkr dj ysrs gSaA
2
(b) fiQj izR;sd ewY; dk oxZ djosQ mu lHkh oxks± dk ;ksx (∑X ) Kkr djrs gSaA
2
(c) Js.kh dk lekUrj ekè; Kkr djosQ mldk oxZ ()X Kkr djrs gSaA
(d) vUr esa izeki fopyu fuEu lw=k }kjk Kkr dj ysrs gSaμ
X
∑ X 2 ∑ F I 2 1 ∑ X 2
()
H K
∑
∑
σ = −G J Or σ = N. X − 2 ( X) 2 Or σ = − X 2
N N N N
tc Js.kh osQ ewY; dkiQh NksVs gksa rks ;g loZJs"B jhfr gSA
mnkgj.k (Illustration) 3:
fuEu Js.kh ls izeki fopyu Kkr dhft,μ
ewY;μ26, 24, 29, 22, 30, 19, 24, 28, 28, 30
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