Page 121 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—8% fo"kerk ,oa i`Fkq'kh"kZRo % dkyZ fi;lZu] ckmys] oSQyh dh fof/;k¡

uksV

VkLd fo"kerk dk izFke eki fdls dgrs gSa \

II. fo"kerk osQ lkis{k eki (Relative Measures of Skewness)

nks Jsf.k;ksa ;k caVuksa dh rqyuk djus osQ fy, fo"kerk osQ lkis{k eki Kkr fd, tkrs gSaA budks fo"kerk xq.kkad
(Coefficient of skewness) Hkh dgrs gSaA lkis{k eki ;k fo"kerk xq.kkad Kkr djus osQ fy, fujis{k eki dks
vifdj.k osQ fdlh Hkh eki ls foHkkftr dj fn;k tkrk gSA ijUrq è;ku jgs] O;ogkj esa osQoy izeki fopyu
dk gh iz;ksx fd;k tkrk gS] D;ksafd vifdj.k osQ vU; eki fdlh&u&fdlh :i esa lhekxzflr gSa tcfd izeki
fopyu ,d vkn'kZ eki gSA
lkis{k fo"kerk osQ izeq[k eki (Main Measures of Relative Skewness)

lkis{k fo"kerk osQ fuEu pkj izeq[k eki gSaμ
(1) dkyZ fi;lZu fo"kerk xq.kkad (Karl Pearson Coefficient of Skewness)
(2) ckmys dk fo"kerk xq.kkad (Bowley’s Coefficient of Skewness),
(3) oSQyh dk fo"kerk xq.kkad (Kelly’s Coefficient of Skewness),

(4) ifj?kkrksa ij vk/kfjr fo"kerk eki (Skewness Measures based on Moments)A
(1) dkyZ fi;lZu fo"kerk xq.kkad (Karl Pearson Coefficient of Skewness)
dkyZ fi;lZu dk eki lekUrj ekè; rFkk cgqyd osQ vUrj ij vk/kfjr gS vkSj foHkktd osQ :i esa izeki
fopyu dk iz;ksx gksrk gSA
X − Z
lw=kkuqlkjμfi;lZu fo"kerk xq.kkad ;k J =
σ
oSdfYid lw=k (Alternative Formula)μ;fn cgqyd vLi"V o vfuf'pr gS rks ekè;ksa osQ ikjLifjd lEcU/
osQ vk/kj ij oSdfYid lw=k dk iz;ksx fd;k tkrk gS tksfd bl izdkj gSμ
3(X − M)
oSdfYid lw=k% J = [Q X – Z = 3(X – M)]
σ
fi;lZu xq.kkad dh fo'ks"krk,¡μ(i) ;fn J dk eku 'kwU; gS rks caVu fo"kerk jfgr vFkkZr~ lefer gksrk gSA (ii)
;fn J dk eku (+) esa gS rks /ukRed fo"kerk vkSj (–) gksus ij Í.kkRed fo"kerk gksrh gSA (iii) fl¼kUr :i esa
bl xq.kkad dh dksbZ lhek ugha gS (tksfd bldk izeq[k nks"k gS) ijUrq O;ogkj esa ;g lkekU;r;k ± 1 osQ chp
jgrk gSA oSdfYid lw=k dh fLFkfr esa xq.kkad dh lhek,¡ ± 3 gksrh gSaA
(2) ckmys dk fo"kerk xq.kkad (Bowley’s Coefficient of Skewness)
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
,d lefer caVu esa nksuksa prqFkZd eè;dk ls leku nwjh ij gksrs gSa vFkkZr~ (M – Q = Q – M)A ;fn ;g vUrj
3
1
leku ugha gS rks caVu esa fo"kerk fuf'pr gSA bu vUrjksa osQ vk/kj ij fd;k x;k eki gh ckmys dk fo"kerk
eki gSA pw¡fd bl eki dk iz;ksx loZizFke MkW- ckmys }kjk fd;k x;k Fkk] blfy, bls ‘Bowley’s Measures
of Skewness’ Hkh dgrs gSaA lw=k bl izdkj gSμ
ckmys dk fujis{k fo"kerk eki ;k fo"kerk dk prqFkZd ekiμ
SK = (Q – M) – (M – Q ) ;k SK = Q + Q – 2M
3
1
1
Q
Q
3
ckmys dk fo"kerk xq.kkad ;k fo"kerk dk prqFkZd xq.kkadμ
LOVELY PROFESSIONAL UNIVERSITY 115