Page 118 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 8-1 fo"kerk dk vFkZ ,oa ifjHkk"kk (Meaning and Definition of Skewness)

fo"kerk dk viuk dksbZ Lora=k vFkZ ugha gksrk gS cfYd bldk iz;ksx lefefr osQ eki osQ :i esa djrs gSaA fdlh
lead Js.kh esa lefefr osQ vHkko dks fo"kerk vFkok vlefefr dgrs gSaA nwljs 'kCnksa esa] fdlh forj.k osQ
lefefr ls nwj gVus dh izo`fÙk fo"kerk dgykrh gSA fo"kerk dh eki ls ;g Kkr gksrk gS fd ;fn vko`fÙk caVu
dk oØ cuk;k tk, rks og lefer gksxk ;k vlefer rFkk vlefefr dh fn'kk o ek=kk D;k gksxhA

ØkWDlVu o dkmMsu osQ vuqlkj] ¶tc dksbZ Js.kh lefer ugha gksrh rks mls vlefer ;k oS"kE; dgk tkrk gSA¸
fjxyeSu o fÚLch osQ vuqlkj] ¶fo"kerk lefefr dk vHkko gSA tc ,d vko`fÙk caVu dks js[kkfp=k dj izkafdr
fd;k tkrk gS rks in&ewY;ksa esa mifLFkr fo"kerk dh izo`fÙk eè;d osQ ,d rjiQ vf/d iSQyus dh gksrh gS u
fd nwljh rjiQA¸
flEilu ,oa dkÝdk (Simpson and Kafka) osQ vuqlkj] ¶fo"kerk osQ eki gesa vlefefr (fo"kerk) dh
fn'kk o lhek crkrs gSaA ,d lefer caVu esa lekUrj ekè;] eè;dk rFkk cgqyd le:i gksrs gSaA lekUrj ekè;
cgqyd ls ftruk nwj gksrk tkrk gS vlefefr ;k fo"kerk mruh vf/d gksrh gSA¸
xSjV osQ vuqlkj] ¶,d caVu fo"ke dgykrk gS tc caVu esa ekè; rFkk eè;dk fHkUu fcUnqvksa ij fLFkr gksrs gSa
vkSj xq#Ro osQUnz (Central of gravity) ,d rjiQ vFkok nwljh rjiQ ck;sa ;k nk;sa f[kld tkrk gSA¸

fo"kerk gksus ij lefer ugha gksrh vkSj lefer gksus ij fo"kerk yqIr gks tkrh gSA

1. lefer caVu ;k forj.k (Symmetrical Distribution)μlefer izÑfr osQ vk/kj ij vko`fÙk caVu
nks izdkj osQ gks ldrs gSaμ(1) lefer] (2) vleferA lefer caVu esa vko`fÙk;ksa osQ c<+us vkSj ?kVus
dk Øe fu;fer gksrk gSA blesa vko`fÙk;k¡ fu;fer Øe ls c<+rh gSa fiQj ,d fuf'pr fcUnq vFkkZr~ vf/
dre vko`fÙk ls mlh fu;fer Øe esa ?kVrh gSaA bldk oØ ?k.Vh osQ vkdkj okyk gksrk gS ftls izlkekU;
oØ dgrs gSaA ,d lefer caVu esa lekUrj ekè;] eè;dk o cgqyd cjkcj gksrs gSa rFkk eè;dk ls nksuksa
prqFkZd ewY;ksa osQ vUrj Hkh vkil esa leku gksrs gSaA (X = M = Z or Q – M = M – Q ) bl caVu esa
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fo"kerk dk eku 'kwU; gksrk gSA
2. vlefer caVu ;k forj.k (Asymmetrical or Skewed Distribution)μvlefer caVu esa vko`fÙk;ksa

osQ c<+us o ?kVus dk Øe fu;fer ugha gksrkA vko`fÙk;k¡ ftl Øe ls igys c<+rh gSa vf/dre gksus osQ
ckn fiQj mlh Øe ls ugha ?kVrhaA ,sls caVu dk oØ ?k.Vkdkj u gksdj nk;sa o ck;sa >qdko fy;s gksrk
gSA ,sls caVu esa lekUrj ekè;] eè;dk ,oa cgqyd dk ewY; cjkcj ugha gksrk vkSj eè;dk ls nksuksa
prqFkZdksa osQ ewY; Hkh vleku gksrs gSaA bl caVu esa fo"kerk ikbZ tkrh gSA ;s nks izdkj osQ gksrs gSaμ

(a) /ukRed fo"kerk (Positive Skewness)μ;fn oØ nkfguh vksj vf/d >qdk gqvk gks rks
fo"kerk /ukRed gksrh gS (nsf[k, fp=k&B)A /ukRed fo"kerk okys caVu esa lekUrj ekè;
(X ) eè;dk (M) ls cM+k gksrk gS vkSj eè;dk cgqyd (Z) ls cM+k gksrk gSA blh izdkj eè;dk
ls r`rh; prqFkZd dk vUrj (Q – M)] eè;dk ls izFke prqFkZd osQ vUrj (M – Q ) ls vf/
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d gksrk gSA

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