Page 172 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV X Y
ekè; (Mean) 31 61

izeki fopyu (Standard Deviation) 3.25 3.35
laxr ekè;ksa ls X rFkk Y osQ fopyuksa osQ xq.kuiQyksa dk ;ksx
(Sum of the products of deviations of X and Y from their respective means) = 75
X vkSj Y osQ tksM+ksa dh la[;k (No. of pairs of X and Y) = 10
gy (Solution):
fn;k gqvk gS % N = 10, σ = 3.25, σ = 3.35
x y
Σd d = 75, X = 31, Y = 61
x y
Σdd 75 75
vr% r = x y = = = 0.69
Nσσ y × 10 . × 3 25 3 35 108 875
.
.
x
mnkgj.k (Illustration) 7: fuEu vkadM+ksa ls σ , σ rFkk X o Y osQ chp lglEcU/ xq.kkad Kkr dhft,&
x
y
X Js.kh (Series) Y Js.kh (Series)
inksa dh la[;k (No. of items) 15 15
lekUrj ekè; (Arithmetic mean) 25 18

ekè; ls fopyu osQ oxks± dk ;ksx 136 138
X rFkk Y Js.kh osQ Øe'k% ekè;ksa ls fy;s x;s fopyuksa osQ xq.kuiQyksa dk ;ksx
= 122
gy (Solution):

2
2
fn;k gqvk gS % N = 15, X = 25, Y = 18, Σd d = 122, Σd = 136, Σd = 138
x y x y
Σdd y 122 122 122
x
vr% r = = = = = .89
.
,
Σ 2 x Σd × d y 2 136 × 138 18 768 136 996
Σd 2 136
σ = n x = 15 = 3.01
x
Σd 2 y 138
σ = n = 15 = 3.03
y

lglEcU/ xq.kkad fudkyus dh y?kq jhfr;ka
(Short-cut Methods for Calculating Coefficient of Correlation)
lglEcU/ fudkyus dh igys crk;h x;h jhfr;ksa esa geus ;g ns[kk fd fofHkUu ewY;ksa osQ fopyu (deviations)
okLrfod lekUrj ekè; (True Arithmetic Average) ls fudkys x;sA ;fn ekè; iw.kk±d gksa rc rks blesa dksbZ
vlqfo/k ughaA ijUrq ;g lnk lEHko ughaA tc ekè; fHkUu esa gksa rks muls fopyu fudkyus vkSj mu fopyuksa
dk oxZ djus] vkfn esa cM+h vlqfo/k gksrh gSA bl vlqfo/k ls cpus osQ fy, y?kq jhfr dk iz;ksx fd;k tkrk
gSA blesa dksbZ iw.kk±d la[;k dfYir ekè; (Assumed Average) osQ :i esa ys yh tkrh gS vkSj mlh ls fopyu
fudkydj izeki fopyu (Standard Deviation) fudky fy;k tkrk gSA dHkh&dHkh iz'u esa ls gh fuf'pr
la[;k dfYir ekè; ysus osQ fy, dgk tkrk gS] vr% ,slh fLFkfr esa mUgha la[;kvksa dks gh dfYir ekè;

166 LOVELY PROFESSIONAL UNIVERSITY