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lkekftd 'kks/ dh i¼fr



                  uksV          Hkfo"; osQ fo"k; esa vuqeku yxkuk gekjs fy, ljy gks tkrk gSA fopyu gesa vius lqfuf'pr fu"d"kZ ls fopfyr
                                gksus ls cpkrk gS] cpkrk gS Hkzeiw.kZ Kku lsA

                                28-1  fopyu ;k fo{ksi.k dh eki (Measures of Variation or Dispersion)


                                fopyu dk vFkZ (Meaning of Variation)
                                fopyu vFkok fo{ksi.k (Dispersion) og xq.k gS ftlls ;g Kkr gksrk gS fd inksa osQ eku muosQ eè;ekuksa
                                (;k ekè;] ewY;ksa) ls fdl lhek rd fopfyr gSaA ;g lp gS fd ekè; ewY;ksa (ekè;] eè;kad o cgqyd)
                                ls lEiw.kZ Js.kh dh osQUnzh; izo`fÙk dk irk yx tkrk gSA ijUrq blosQ }kjk Js.kh osQ fofHkUu inewY;ksa
                                dk iw.kZ rFkk fuf'pr Kku fo'ks"kdj ml voLFkk esa ugha gks ikrk gS tcfd eè;eku rFkk vU; inewY;ksa
                                esa vf/d vUrj gksrk gSA O;kogkfjd n`f"Vdks.k ls ns[kk tk;s rks vusd LFky ,sls vkrs gSa tgk¡ eè;eku
                                Hkzked ifj.kke iznku djrk gSA mnkgj.kkFkZ % ;fn fdlh ifjokj osQ ikap O;fDr;ksa dh vkenuh ozQe'k%
                                20] 60] 200] 50 vkSj 70 #i;s gks rks mudh vkenuh dk eè;eku 80 #ú gqvkA ;fn gesa bu ikapksa
                                vkadM+ksa dk i`Fko~Q&i`Fko~Q Kku u gks rks eè;eku osQ vk/kj ij ge ;gh le>saxs fd ifjokj osQ izR;sd
                                O;fDr dh vkenuh 80 ;k 80 #i;s osQ vklikl gksxh tcfd okLrfod fLFkfr blls dgha fHkUu gSA vr%
                                ,slh n'kkvksa esa fdlh ,sls eki (Measure) dh vko';drk iM+rh gS tks vf/d&ls&vfèkd inewY;ksa
                                dh tkudkjh djk ns vFkkZr~ inewY;ksa dk eè;eku ls fdruk fopyu gSA bUgha ekiksa dks fopyu osQ eki
                                dgk tkrk gSA
                                fopyu osQ vFkZ dks ,d vkSj mnkgj.k }kjk Li"V fd;k tk ldrk gSA eku yhft,] nks fo|kfFkZ;ksa osQ
                                pkj fo"k;ksa esa izkIrkad 28] 60] 60] 92 vkSj 56] 60] 60] 64 gSa tcfd izR;sd fo"k; esa iw.kk±d 100
                                vkSj ikl gksus osQ fy;s 33 vad vko';d gSaA bu fo|kfFkZ;ksa osQ Lrj dks tkuus osQ fy, ;fn lekUrj
                                ekè; Kkr djsa rks mldk eku nksuksa fo|kfFkZ;ksa osQ fy, 60 vkrk gSA vr% bl vk/kj ij nksuksa fo|kfFkZ;ksa
                                dk Lrj leku izrhr gksrk gS] tcfd okLro esa ,slk ugha gS D;ksafd igyk fo|kFkhZ igys fo"k; esa vuqÙkh.kZ
                                (failed) gS] tcfd nwljk fo|kFkhZ izR;sd fo"k; esa mÙkh.kZ gSA vr% Li"V gS fd osQoy eè;eku osQ vkèkkj
                                ij gh Js.kh osQ Li:i dk iw.kZ Kku ugha gks ldrkA





                                   D;k vki tkurs gSa  ;g Hkh tkuuk vko';d gS fd Js.kh dk izR;sd in ekè; ls fdruh nwjh ij gS ;k fdruk
                                                  fc[kjk gqvk gSA bl fc[kjko dks gh fopyu ;k fo{ksi.k dgrs gSaA


                                fopyu dh ekisa (Measuring of Dispersion)

                                fopyu dh eq[; ekisa bl izdkj gSaµ
                                (1) ifjlj  (Range)

                                (2) prqFkk±'kh; fopyu  (Quartile Deviation)
                                (3) ekè; fopyu  (Mean Deviation)
                                      (d) lekUrj ekè; ls

                                      ([k) eè;kad ls
                                      (x) cgqyd ls
                                (4) ekud fopyu  (Standard Deviation)




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