Page 140 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 1525
=
9. 1500 . 1580
9 9
1525 1525
= =
9 × × 12.91 13.25 1539.55
= + .99

Σdxdy
r`rh; lw=k osQ vuqlkj r =
Σ 2 Σdx . dy 2
1525 1525
= =
1500 × 1580 1539.5
= + .99
bl izdkj rhuksa lw=kksa ls izkIr ifj.kke leku gSaA ;g + .99 gS vFkkZr ifr ,oa ifRu;ksa dh vk;q esa vR;f/d
?kukRed lglEcU/ gSA
izR;{k jhfr esa y?kqx.kdksa dk iz;ksxμr`rh; lw=k osQ iz;ksx osQ le; y?kqx.kdksa osQ ekè;e ls x.ku fØ;k dks
vkSj ljy cuk;k tk ldrk gSA y?kqx.kdksa osQ iz;ksx dh izfØ;k fuEukuqlkj gSμ
2
r = Antilog [Log Σdxdy – ½ (Log Σdx + Log Σdy )]
2
mDr mnkgj.k dks y?kqx.kdksa osQ iz;ksx }kjk fuEu izdkj gy fd;k tk,xkμ
r = Antilog [Log .1525 – ½ (Log .1500 + Log .1580)]
= Antilog [3.1832 – ½ (3.1761 + 3.1987)]
= Antilog [ 1 9958. ]
= + .99
y?kq jhfr (Short-cut Method)

izR;{k jhfr esa lglEcU/ xq.kkad Kkr djrs le; okLrfod vadxf.krh; ekè; ls fopyu Kkr fd, tkrs gSa]
blfy, tc vadxf.krh; ekè; iw.kk±d esa gks mlh le; izR;{k jhfr mi;qDr jgrh gS] fdUrq tc vadxf.krh;
ekè; n'keyo esa gks rks ,sls le; izR;{k jhfr osQ iz;ksx ls x.ku fØ;k,¡ cgqr tfVy gks tkrh gSa] vr% y?kq
jhfr osQ iz;ksx }kjk lglEcU/ xq.kkad dh x.kuk dh tkrh gSA y?kq jhfr esa lead Js.kh osQ fopyu dfYir ekè;
2
2
ls Kkr fd, tkrs gSa] vr% ckn osQ lw=k esa Σdxdy, Σdx ,oa Σdy esa vko';d la'kks/u dj fy, tkrs gSaA y?kq
jhfr }kjk lglEcU/ xq.kkad Kkr djus dh izfØ;k fuEu izdkj gSμ
(i) loZizFke nksuksa lead Jsf.k;ksa esa ls ,d&,d mi;qDr ewY; dks dfYir ekè; ekudj mlls fopyu Kkr
dj fy, tkrs gSaμ
dx = (X – A ), dy = (Y – A )
x y
(ii) izkIr fopyuksa dk ;ksx Øe'k% Σdx ,oa Σdy Kkr dj fy;k tkrk gSA
2
2
2
(iii) dfYir ekè;ksa ls Kkr fopyuksa dk oxZ djosQ dx ,oa dy rFkk budk ;ksx djosQ Σdx ,oa Σxy 2
Kkr dj fy, tkrs gSaA
(iv) dfYir ekè;ksa ls Kkr fopyuksa dks vkil esa xq.kk djosQ (dxdy), buosQ xq.kuiQy dk ;ksx Σdxdy Kkr
fd;k tkrk gSA

(v) fuEu izFke lw=k osQ iz;ksx osQ le; lead Jsf.k;ksa osQ vadxf.krh; ekè; ( X , Y ) rFkk izeki fopyu
(σ , σ ) Hkh Kkr dj fy, tkrs gSaA
x
y

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