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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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