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vFkZ'kkL=k esa lkaf[;dh; fof/;k¡
uksV (2) foHkktu&ewY;ksa dk vUrjμ;fn eè;dk ls nksuksa prqFkZd leku nwjh ij u gksa vFkkZr~ (Q – M) ≠
3
(M – Q ) vFkok (Q – M) – (M – Q ) = 0 u gksa rks Js.kh esa fo"kerk ikbZ tkrh gSA
1
3
1
(3) fopyuksa dk ;ksxμ;fn eè;dk vkSj cgqyd ls fy, x, fopyuksa dk chtxf.krh; ;ksx 'kwU; u gks
(Σd ≠ 0) rks caVu esa fo"kerk gksrh gSA
(4) oØ dk Lo:iμcaVu dks js[kkfp=k ij vafdr djus ij ;fn oØ ?k.Vkdkj ugha gS vFkok og nk;sa ;k
ck;sa vf/d >qdko fy, gS rks mlesa fo"kerk gksrh gSA
(5) vko`fÙk;ksa dk iSQykoμ;fn cgqyd osQ nksuksa vksj dh vko`fÙk;ksa dk ;ksx cjkcj ugha gS rks Js.kh esa
fo"kerk gksrh gSA
Lo&ewY;kadu (Self Assessment)
1- fjDr LFkkuksa dh iw£r djsa (Fill in the blanks)μ
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1. lefer caVu esa vko`fÙk;ksa osQ c<+us vkSj ?kVus dk gksrk gSA
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2. lefer caVu dk oØ ?k.Vh osQ vkdkj okyk gksrk gS ftls dgrs gSaA
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3. vlefer caVu dk oØ ?k.Vkdkj u gksdj >qdko fy;s gksrk gSA
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4. ;fn oØ nkfguh vksj vf/d >qdk gqvk gks rks fo"kerk gksrh gSA
5. --------- esa lekUrj ekè; dk ewY; eè;dk ls de vkSj eè;dk dk ewY; cgqyd ls de gksrk gSA
8-2 fo"kerk osQ eki (Measures of Skewness)
Åij crk, x, ijh{k.k (tests) osQoy bl ckr dk laosQr nsrs gSa fd dksbZ caVu&fo'ks"k fo"ke gS vFkok ughaA
blosQ ckn vxyh leL;k gksrh gS fo"kerk ;k vlefefr dh ek=kk ;k lhek (Extent) dh eki djukA blosQ fy,
fo"kerk osQ eki iz;ksx esa yk, tkrs gSaA ;s eki nks izdkj osQ gksrs gSaμfujis{k eki rFkk lkis{k ekiA
I. fo"kerk osQ fujis{k eki (Absolute Measures of Skewness)
bUgsa fo"kerk osQ izFke eki (First Measures of Skewness) Hkh dgrs gSaA fujis{k eki bl ekU;rk ij vkèkkfjr
gS fd ,d fo"ke caVu esa lekUrj ekè;] eè;dk rFkk cgqyd ewY; leku ugha gksrsA vr% buesa ls fdUgha nks
ewY;ksa (ekè;ksa) osQ chp dk vUrj] fo"kerk dh ek=kk gksrh gSA lw=kkuqlkjμ
fujis{k fo"kerk ;k S = X – Z ;k S = X – M ;k S = M – Z
k k k
fVIi.khμtc fo"kerk dk eki prqFkZdksa ij vk/kfjr gks rc fujis{k fo"kerk dk lw=k fuEu gSμ
fujis{k fo"kerk ;k S = Q + Q – 2M
3
k
1
fo"kerk osQ fujis{k (;k izFke) eku fuEu dkj.kksa ls vlarks"ktud ekus tkrs gSaμ
(1) caVuksa dh bdkb;k¡ fHkUu gksukμfujis{k eki mlh bdkbZ esa O;Dr gksrh gS tks ml caVu fo'ks"k dh bdkbZ
gksrh gSA pw¡fd caVuksa dh bdkb;k¡ izk;% fHkUu&fHkUu gksrh gSa vr% tc ge ,d caVu dh fo"kerk dh
rqyuk fdlh vU;=k bdkbZ okys caVu ls djuk pkgsa rks og lEHko ugha gks ikrkA mnkgj.kkFkZ] Nk=kksa osQ
Hkkj vkSj mudh yEckbZ okyh nks Jsf.k;ksa osQ chp fujis{k fo"kerk dh rqyuk ugha dh tk ldrh] D;ksafd
nksuksa dh bdkb;k¡ fHkUu&fHkUu gSA
(2) caVuksa rFkk ekè;ksa esa vR;f/d vUrj gksukμcaVuksa esa izk;% vR;f/d fHkUurk gksrh gSA nks ekè;ksa dk
fujis{k vUrj (X – Z or X – M) fdlh ,d caVu esa cgqr T;knk gks ldrk gS tcfd nwljs caVu esa leku
gks] ijUrq mu nksuksa caVuksa dks ;fn js[kkfp=k ij izkafdr fd;k tk, rks muosQ oØ le:i (similar) Hkh
gks ldrs gSaA
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