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vFkZ'kkL=k esa lkaf[;dh; fof/;k¡




                    uksV          (ii) [kf.Mr pj (Discrete Variables)μv[kf.Mr osQ foijhr [kf.Mr pj os gSa ftuosQ ewY; fuf'pr vkSj
                                  [kf.Mr gksrs gSaA vFkkZr buesa foLrkj ugha gksrk cfYd ,d ewY; ls nwljs ewY; osQ chp oqQN lqfuf'pr vUrj
                                  (definite break or gap) gksrk gSA bl izdkj [kf.Mr pj dh bdkb;k¡ foHkkT; ugha gksrha vFkkZr foLrkj jfgr
                                  gksrh gSaA mnkgj.kkFkZ] nq?kZVukvksa dh la[;k 0, 1, 2, 3, gksxh] vkèkh] pkSFkkbZ ;k n'keyoka'k esa ughaA blh izdkj
                                  ifjokj esa cPpksa dh la[;k] fØosQV juksa dh la[;k] izfr i`"B xyfr;ksa dh la[;k vkfn [kf.Mr pj osQ mnkgj.k
                                  gSaA rqyuk dh n`f"V ls uhps nksuksa izdkj osQ pjksa ij vkèkkfjr vko`fr forj.k fn[kk;k x;k gSμ
                                           v[kf.Mr vko`fÙk forj.k                    [kf.Mr vko`fÙk forj.k

                                     Hkkj (fdyks- esa)  O;fDr;ksa dh la[;k   cPpksa dh la[;k     ifjokjksa dh la[;k
                                         40–50                 30                  0                   10
                                         50–60                145                  1                   22
                                         60–70                210                  2                   75
                                         70–80                 60                  3                  160
                                         80–90                 10                  4                  140
                                        90–100                 5                   5                   43

                                         ;ksx                 460                 ;ksx                450

                                  uksVμlrr pj ls cuus okyh Jsf.k;ksa dks lrr jsf.k;k¡ dgrs gSa vkSj [kf.Mr pjksa }kjk O;Dr Jsf.k;k¡] [kf.Mr
                                  jsf.k;k¡ dgykrh gSaA
                                  3-5 vko`fÙk forj.k dh jpuk (Formation of Frequency Distribution)


                                  mi;qZDr fooj.k ls Li"V gS fd vko`fÙk&forj.k] [kf.Mr ,oa v[kf.Mr pjksa dk lqcksèk ,oa laf{kir :i esa
                                  izLrqrhdj.k gSA bl n`f"V ls vko`fÙk&forj.k dh jpuk Hkh fuEu nks :iksa esa dh tkrh gSμ(i) [kf.Mr vko`fÙk
                                  forj.k rFkk (ii) v[kf.Mr vko`fÙk forj.kA
                                  (i) [kf.Mr vko`fÙk forj.k (Discrete frequency distribution)μtSlk fd blosQ uke ls Li"V gS] bl
                                  forj.k esa [kf.Mr pjksa osQ vkèkkj ij vko`fÙk rkfydk dk fuekZ.k fd;k tkrk gSA bldh jpuk&fofèk cgqr ljy
                                  gSμ(i) loZ izFke vO;ofLFkr leadksa (raw data) dks vkjksgh (ascending) ;k vojksgh (descending) de esa
                                  ltk fy;k tkrk gSA bl fØ;k dks Øe&foU;kl (array) dgrs gSaA (ii) fiQj] pj osQ lHkh lEHkkO; ewY; (vFkkZr~
                                  lcls NksVs ls ysdj lcls cM+k ewY;) rkfydk osQ izFke dkWye esa Øe&okj fy[k fy;s tkrs gSaA bUgsa in&ewY;
                                  dgrs gSaA (iii) blosQ ckn ^feyku&fpÉksa* ;k ^VSyh&ckj* (Tally-marks or Tally-bars) dh lgk;rk ls izR;sd
                                  in&ewY; dh vko`fÙk Kkr dj yh tkrh gSA bls uhps fn;s x;s mnkgj.k ls le>k tk ldrk gSA
                                  mnkgj.k (Illustration) 1: bUnkSj osQ ,d 'kks&:e }kjk fdlh ,d fnu csph x;h 30 dehtksa osQ lkbt (lseh-
                                  esa) bl izdkj gSaμ
                                   34   32    36   30    33   34   34    29   36    35   30   30    32   35    33
                                   31   31    34   35    34   35   30    36   32    32   32   29    34   34    33
                                  mi;qZDr dh lgk;rk ls ,d [kf.Mr vko`fÙk forj.k rS;kj dhft;sA
                                  gy (Solution): pw¡fd deht dk lcls NksVk lkbt 29 lseh- vkSj lcls cM+k lkbt 36 lseh- gSA vr% igys
                                  29 ls 36 rd osQ in&ewY; c<+rs gq, Øe esa fy[k fy;s tk;saxsA vc ;g ns[kuk gS fd fdl&fdl lkbt dh
                                  fdruh&fdruh dehtsa fcdh gSa] vFkkZr~ izR;sd in&ewY; dh vko`fÙk D;k gS\ lcls igyh deht 34 ua- dh
                                  fcdh gSaA vr% 34 lkbZt osQ lkeus feyku js[kkvksa okys dkWye esa ,d ^ckj* ;k ^[kM+h ydhj* [khap nsaxsA blosQ



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