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vFkZ'kkL=k esa lkaf[;dh; fof/;k¡



                   uksV          x;s fu"d"kZ vfuf'pr ,oa HkzekRed gks ldrs gSaA bu lhekvksa ,oa HkzekRed fu"d"kks± osQ dkj.k lkaf[;dh dh
                                 vkykspuk,¡ Hkh gksrh gSa ijUrq lhek,¡ izR;sd foKku dh gksrh gSa pkgs og vFkZ'kkL=k gks HkkSfrd ;k jlk;u'kkL=kA
                                 lkaf[;dh dh lhekvksa esa jgrs gq, ;fn fo'ys"k.k ,oa fuoZpu fd;k tk, rks lhekvksa osQ dkj.k  mRiUu nks"kksa dks
                                 lekIr fd;k tk ldrk gSA izks- U;wtgkse osQ vuqlkj] ¶lkaf[;dh dks vuqlU/ku dk ,d vR;Ur ewY;oku lkèku
                                 le>uk pkfg,] ijUrq bldh oqQN xEHkhj lhek,¡ gSa ftUgsa nwj fd;k tkuk rks lEHko ugha gS vkSj blfy, bu ij
                                 gesa lko/kuh ls fopkj djuk pkfg,A¸
                                 lkaf[;dh dh fuEu lhek,¡ gSaμ
                                 1. lkaf[;dh osQoy la[;kRed rF;ksa dk gh vè;;u djrh gS] xq.kkRed rF;ksa dk ugha (Statistics studies
                                 quantitative phenomena and not qualitative)μlkaf[;dh dh izeq[k lhek ;g gS fd ;g osQoy la[;kRed
                                 :i ls O;Dr fd;s x;s rF;ksa ;k leL;kvksa dk fo'ys"k.k djrk gS xq.kkRed dk ughaA lkaf[;dh osQ vUrxZr
                                 la[;kRed :i esa o£.kr rF;_ tSlsμvk;q] Å¡pkbZ] mRiknu] ewY;] vk;] tula[;k] ctV vkfn dk izR;{k
                                 fo'ys"k.k fd;k tk ldrk gS ijUrq xq.kkRed :i esa O;Dr rF;_ tSlsμckSf¼d Lrj] pfj=k] lqUnjrk] LokLF;]
                                 xjhch] O;ogkj vkfn dk lkaf[;dh; fo'ys"k.k ugha fd;k tk ldrk gSA bu leL;kvksa dk vè;;u lkaf[;dh
                                 esa ijks{k :i ls fd;k tk ldrk gSA mnkgj.k osQ fy,] ckSf¼d Lrj dk vuqeku ijh{kk esa izkIr izkIrkadksa osQ vk/
                                 kj ij] LokLF; lEcU/h tkudkjh tUenj ,oa e`R;qnj osQ fo'ys"k.k osQ }kjk izkIr dh tk ldrh gSA
                                 2. lkaf[;dh lewgksa dk vè;;u djrh gS] O;fDrxr bdkb;ksa dk ugha (Statistics deals with aggregates
                                 but not with individuals)μlkaf[;dh esa fdlh Hkh {ks=k dh lkewfgd fo'ks"krkvksa dk vè;;u fd;k tkrk gS
                                 O;fDrxr bdkbZ dk ughaA ;|fi vè;;u djrs le; O;fDrxr bdkb;ksa dks gh ekè;e cuk;k tkrk gS ijUrq
                                 fudkys x;s fu"d"kZ ,d vkSlr ,oa lewg dh izÑfr n'kkZrs gSaA mnkgj.k osQ fy,] fdlh ns'k dh izfr O;fDr vk;
                                 lkewfgd fo'ks"krkvksa ij izdk'k Mkyrh gSA ;g lekt osQ vyx&vyx oxks±_ tSlsμvehj] xjhc] fHk[kkjh]
                                 djksM+ifr vkfn dh O;fDrxr vk; ugha crkrh gSA izks- uht cSaxj osQ vuqlkj] ¶lkaf[;dh osQ fu"d"kZ lewg osQ
                                 lkewfgd O;ogkj dk vuqeku yxkus esa lgk;d gksrs gSa ml lewg dh O;fDrxr bdkb;ksa dk ughaA¸ mnkgj.k osQ
                                 fy,] lkaf[;dh osQ }kjk ;g rks Kkr gks tkrk gS fd izfr O;fDr pkoy ;k xsgw¡ dh [kir ,d fnu es fdruh
                                 gS ijUrq ;g Kkr ugha gksrk fd xjhcksa esa pkoy ;k xsg¡w dh fdruh deh gSA
                                 3. lkaf[;dh; jhfr fdlh leL;k osQ vè;;u dh ,dek=k jhfr ugha gS (Statistics is not only a single
                                 method used for study of any problem)μlkekU; thou esa fdlh Hkh leL;k osQ lek/ku dh vusd jhfr;k¡
                                 gksrh gSa ftuesa ls lkaf[;dh ,d jhfr gSA lkaf[;dh; fo'ys"k.k osQ }kjk izkIr fu"d"kks± dks rHkh vfUre lR; ekuuk
                                 pkfg, tc os vU; jhfr;ksa_ tSlsμiz;ksx] vUrjkoyksdu] fuxeu rFkk vU; izek.kksa }kjk iw.kZr;k tk¡p fy;s tk,¡A
                                 ØkWDlVu ,oa dkmMsu osQ vuqlkj] ¶;g ugha eku ysuk pkfg, fd lkaf[;dh; jhfr gh vuqlUèkku dk;Z esa iz;ksx
                                 dh tkus okyh ,dek=k jhfr gS] u gh bl jhfr dks izR;sd izdkj dh leL;k dk loksZÙke gy le>uk pkfg,A¸
                                 ysfdu fiQj Hkh lakf[;dh ,d mi;ksxh 'kL=k gS D;ksafd ;FkkFkZrk ,oa 'kq¼rk osQ cgqr fudV gksrk gSA MkW- ckmys
                                 osQ vuqlkj] ¶lkaf[;dh; eki fdlh leL;k osQ lekèkku osQ fy, mruk gh vko';d gS ftruk ,d Hkou&fuekZ.k
                                 osQ fy, ;FkkFkZ ekiA¸
                                 4. lkaf[;dh osQ fu"d"kZ vlR; o HkzekRed gks ldrs gSa ;fn mudk fo'ys"k.k fcuk lUnHkZ osQ fd;k tk,
                                 (Statistical results may be misleading and ambiguous if analysed without proper
                                 context of the problem)μlkaf[;dh osQ fu"d"kks± dks le>us osQ fy, leL;k osQ gj igyw ls okfdiQ gksuk
                                 vko';d gS vU;Fkk os Hkzked gks ldrs gSaA leL;k dh izR;sd ifjfLFkfr ,oa lUnHkZ dks tkuus osQ i'pkr~ fudkys
                                 x;s fu"d"kZ gh okLrfod :i ls lR; gksrs gSa vU;Fkk fcuk leL;k dks le>s fudkys x;s fu"d"kZ okLrfod fn[kkbZ
                                 rks nsrs gSa ijUrq okLrfod gksrs ugha gSaA mnkgj.k osQ fy,] fdUgha nks m|ksxksa osQ fiNys ik¡p o"kZ dk vkSlr ykHk




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