Page 145 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—9% lglacaèk% ifjHkk"kk] izdkj ,oa vFkZ'kkfL=k;ksa dh iz;qDr fof/;k¡

vksj osQ izFke [kkus esa X Js.kh osQ dfYir ekè; ls izkIr fopyu (dx) fy[ks tkrs gSa] budk ;ksx Øe'k% uksV
Σdy ,oa Σdx Kkr dj fy;k tkrk gSA
(iii) nk;ha vksj osQ nwljs [kkus esa dy dks rRlEcU/h vko`fr;ksa ls xq.kk djosQ (fdy) fy[kk tkrk gSA uhps dh vksj
osQ nwljs [kkus esa fdx fy[kk tkrk gSA budk ;ksx Σfdy ,oa Σfdx dj fy;k tkrk gSA
2
(iv) nk;ha vksj osQ rhljs [kkus esa fdy dks dy ls xq.kk djosQ fdy rFkk uhps dh vksj osQ rhljs [kkus esa fdx dks
2
2
2
dx ls xq.kk djosQ fdx fy[kk tkrk gS vkSj budk ;ksx Σfdy rFkk Σfdx dj fy;k tkrk gSA
(v) pkSFkk [kkuk Σfdxdy osQ fy, gksrk gS] bldh x.kuk osQ fy, loZizFke lHkh vko`fr;ksa osQ dks"Bksa (cells)
osQ fy, muls lEcfU/r dx ,oa dy dks xq.kk djosQ ml dks"B osQ Åij ck,¡ dksus esa fy[k fn;k tkrk
gSA tSls ,d vko`fr dks"B dk dx – 2 ,oa dy Hkh – 2 gS rks dxdy = 4 gksxkA ;fn mldh vko`fr 5 gS rks
fdxdy dk eku 20 gksxkA bl izdkj vko`fr;ksa osQ lHkh dks"Bksa osQ fy, tc dxdy Kkr dj fy;k tkrk gS
rks izR;sd dks"B osQ dxdy dks ml dks"B dh vko`fr ls xq.kk djosQ uhps nk,¡ dksus esa fdxdy fy[k fn;k
tkrk gSA
mnkgj.kμ dy (– 2)
4(dxdy )
5( ) f
(fdxdy ) 20

dx (– 2)

bl izdkj fdxdy Kkr dj budk {kSfrt tksM+dj nkfguh vksj osQ vfUre [kkus esa fy[k fn;k tkrk gSA budk mnxz
tksM+ Hkh fd;k tk ldrk gS] ,sls le; uhps dh vksj rhu osQ LFkku ij pkj [kkus cukus gksaxsA

(vi) fuEu lw=k osQ iz;ksx }kjk lglEcU/ xq.kkad dh x.kuk dh tkrh gSμ
)(
Σfdxdy − − N(X x Y − A A y)
izFke lw=kμ r =
N . σσ y
x
bl lw=k dk iz;ksx O;ogkj esa cgqr de fd;k tkrk gS_ lkekU;r;k bl lw=k osQ fuEu ljy :i iz;ksx esa yk,
tkrs gSa ftuesa Js.kh osQ izeki fopyu ,oa vadxf.krh; ekè; dh x.kuk vyx ls ugha djuh iM+rh gSA

Σfdxdy − G F Σ J G ΣfdxI F fdyI J
N
H N K H N K
f}rh; lw=kμ r =
L 2 Σfdx F 2 O L ΣI 2 Σfdy F fdyI 2 O
N M Σ −G fdx J P × − M G J P
M N N H N K P M N H N K P Q
Q N
Σ Σfdx fdy
Σfdxdy −
r`rh; lw=kμ r = N
L Σfdx OL Σfdy O
2
2
M Σfdx − ( ) PM Σfdy − ( ) P
2
2
N M N Q P N M N Q P
N . Σ ( fdx . Σ− fdy )
Σfdxdy
prqFkZ lw=kμ r =
2
2
Σfdx −
Σfdy −
[ N . Σ 2 ( fdx ) ][ N . Σ 2 ( fdy ) ]
laosQrk{kjksa dk vFkZ iwoZor~ gS] fliZQ buesa vko`fr;ksa (f ) dk lekos'k gqvk gSA
oxhZÑr vko`fr Js.kh esa oxZ&foLrkj osQ leku gksus ij in&fopyu jhfr osQ iz;ksx }kjk Hkh lglEcU/ xq.kkad
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