Page 122 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV (Q − 3 M ) − (M − Q 1 ) Q + 3 Q − 1 2M
J = (Q − 3 M ) + (M − Q 1 ) ;k J = Q − Q 1
Q
Q
3

uksV~l izks- ckmys dk fo"kerk xq.kkad prqFkZdksa vkSj eè;dk ij vk/kfjr gSA bls fo"kerk dk f}rh; eki
Hkh dgrs gSaA

Lej.kh; rRoμ(1) ;g xq.kkad Hkh ,d 'kq¼ vad gSA (2) bl xq.kkad dh lS¼kfUrd lhek,¡ ± 1 gksrh gSaA (3) ,d
lefer caVu dh fLFkfr esa xq.kkad dk eku 'kwU; gksxkA (4) ckmys vkSj fi;lZu osQ fo"kerk xq.kkad osQ eku leku
ugha gksrs cfYd vlk/kj.k vkÑfr okys caVuksa dh fLFkfr esa buosQ foijhr fpÉ Hkh gks ldrs gSaA iQyr% ;s nksuksa
xq.kkad rqyuh; ugha gSaA
ckmys eki dh lhek,¡ (Limitations)μ;g fo"kerk dh ,d ljy eki gS] ijUrq blosQ ifj.kke fo'oluh; ugha
gksrsA mnkgj.kkFkZ] xq.kkad dk eku dbZ ckj 'kwU; gksus ij Hkh] caVu iw.kZr;k lefer ugha gksrkA bldk dkj.k ;g
gS fd prqFkZd Js.kh osQ lHkh ewY;ksa ij vk/kfjr ugha gksrsA nwljs 'kCnksa esa] ;g eki Js.kh osQ osQoy vk/s (50%)
Hkkx dh fo"kerk dk gh vè;;u djrk gSA
(3) oSQyh dk fo"kerk xq.kkad (Kelly’s Coefficient of Skewness)
oSQyh dk fo"kerk xq.kkad ckmys lw=k dk la'kksf/r :i gSA ckmys lw=k tksfd prqFkZdksa ij vk/kfjr gS] osQ vUrxZr
caVu osQ izFke 25% vkSj vafre 25% ewY; NksM+ fn, tkrs gSaA pw¡fsd ,d vPNk eki og gS tks caVu osQ lHkh
ewY;kas ij vk/kfjr gks vr% bl n`f"V ls oSQyh us prqFkZdksa osQ LFkku ij n'kedksa ;k 'kredksa osQ iz;ksx dk lq>ko
fn;k gSA oSQyh us vius fo"kerk lw=k esa izFke rFkk uosa n'ked vFkok nlosa rFkk uCcsosa 'kred dk iz;ksx fd;k
gSA Li"V gS fd bl fLFkfr esa caVu osQ izFke 10% vkSj vafre 10% vFkkZr~ oqQy 20% ewY; vè;;u ls ckgj jgrs
gSa tcfd 80% ewY; vè;;u esa 'kkfey gksrs gSaA oSQyh dk lw=k fuEu gSμ
D + D − 2 M P + P − 2 M
J = 1 D − 9 D 1 or J = 10 P 90 − 90 P 10
K
K
9
D + D − 2 D P + P − 2P
or J = 1 D − 9 D 1 5 or J = 10 P 90 90 P 10 50
−
K
K
9
ge tkurs gSaμD = P , D = P , M = D – P
1 10 9 90 5 50
(4) ifj?kkrksa ij vk/kfjr fo"kerk eki (Skewness Measures based on Moments)
bl jhfr esa ekè; ij vk/kfjr r`rh; ifj?kkr dh lgk;rk ls fo"kerk dk eki Kkr dh tkrh gSA
8-3 vifdj.k vkSj fo"kerk esa vUrj (Difference Between Dispersion and
Skewness)

(1) vifdj.k ls fdlh caVu dh cukoV dk Kku gksrk gSA ljy 'kCnksa esa] vifdj.k dh ekiksa ls bl ckr
dk irk pyrk gS fd Js.kh osQ fofHkUu in&ewY;ksa dk vkil esa ;k fdlh ekè; ls fdruk fopyu ;k
fc[kjko gSA blosQ foijhr fo"kerk osQ eki ;g crkrs gSa fd Js.kh osQ ekè; ls nksuksa vksj osQ Hkkxksa dk
fopj.k cjkcj gS vU;Fkk fdl Hkkx esa fopj.k vf/d gSA
(2) vifdj.k bl ckr dh dksbZ tkudkjh ugha nsrk fd ekè; ls fdl fn'kk esa ewY;ksa dk fopj.k vf/d
gS tcfd fo"kerk dh lgk;rk ls ekè; osQ nksuksa vksj osQ Hkkxksa osQ fopj.k dh rqyuk vFkkZr~ /ukRed
vkSj Í.kkRed fo"kerk osQ :i esa lgt gh dh tk ldrh gSA

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