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'kSf{kd ekiu rFkk ewY;kadu




                    uksV          âkbV us inksa osQ vad vkSj ijh{kk£Fk;ksa osQ izkIrkadksa osQ vkèkkj ij f}ekxhZ dkjdh; izk:i cuk;k vkSj mlesa pfjrk
                                  fo'ys"k.k izfofèk dk iz;ksx djosQ fo'oluh;rk xq.kd dks Kkr djus dh fofèk dk fodkl fd;kA fo'oluh;rk Kkr
                                  djus osQ fy, âkbV us tks ewylw=k fn;k og bl izdkj gSμ
                                                                     V    V −  V
                                                               r  = 1 –   V r e  =  e V e  r
                                                               n
                                  tcfd   r  = fo'oluh;rk xq.kd
                                          tt
                                         V  = ijh{kkFkhZ pfjrk
                                          e
                                         V = 'ks"k osQ ;ksx osQ oxZ dh pfjrk
                                          t
                                                                          Σ
                                                                    Σ  X 2  ( X ) 2
                                                                 2
                                                               Σd  =   n i  −  n N t
                                                                 e
                                          2
                                  tcfd Σd = ijh{kkFkhZ osQ izkIrkadksa osQ oxksZ dk ;ksx
                                          e
                                         X = izR;sd ijh{kkFkhZ osQ izkIrkad
                                          t
                                          n = ijh{k.k esa inksa dh la[;k
                                         N= U;kn'kZ esa ijh{kkFkhZ dh la[;k
                                                                          Σ
                                                                    Σ  R 2  ( X ) 2
                                                                 2
                                                               Σd =   N i  −  Nn t
                                                                 t
                                  tcfd  Σd = inksa osQ vadksa osQ oxZ dk ;ksx
                                          i
                                         R = lgh mÙkjksa dh la[;k
                                          i
                                          2
                                        ΣX = lEiw.kZ izkIrkadksa osQ oxksZ dk ;ksx
                                          t
                                         N= U;kn'kZ esa ijh{kk£Fk;ksa dh la[;k
                                                                    (R )( W )
                                                                     Σ
                                                                          Σ
                                                                 2
                                                               ΣX  =   Σ  R +  i i  Σ  W i i
                                                                 t
                                         W = xyr mÙkjksa dh la[;k
                                          i
                                                                 2
                                                                      2
                                                               ΣX  =  ΣX  – (Σd  + Σd ) i  2
                                                                           e
                                                                      i
                                                                 r
                                  tcfd   X = 'ks"k vad
                                          i
                                                              pfjrk fo'ys"k.k dh rkfydk
                                     pfjrk dk          va'k dh         oxks± dk ;ksx    oxks± osQ ;ksx dk eè;eku
                                       Ïksr             Lora=krk
                                                                                         2
                                     ijh{kkFkhZ V e  (N – 1)            ΣX 2 e         [ΣX / (N – 1)] = V e
                                                                                          e
                                                                                          2
                                     in V i         (n – 1)             ΣX i 2         [ΣX  / (n – 1)] = V i
                                                                                          i
                                                                                         2
                                     'ks"k V e      (N – 1) (n – 1)     vUrj           [SX  / (N – 1) (n – 1)] = V r
                                                                                         r
                                     ;ksx V         (N – 1) + (n – 1)   ΣX 2
                                          X                               i
                                                    + (N – 1) (n – 1)
                                                                   V −  V   Σ  2  −  Σ d  d 2
                                                               r  =   e  r  =  e    r
                                                               tt    V e       Σd 2 e
                                  âkbV dh fofèk dks Li"V djus gsrq ,d mnkgj.k ;gk¡ fn;k x;k gS ftldh lgk;rk ls bls Li‘ le> ldrs gSaA



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