Page 65 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZμ5 % ekè;] ekfè;dk rFkk cgqyd osQ vuqiz;ksx

(ii) fiQj] izR;sd in&ewY; esa ls dfYir&ekè; fopyu izkIr dj fy;s tkrs gSa vFkkZr~ dx = (X – A)A uksV
(iii) izR;sd fopyu (dx) dks mldh vko`fÙk (f) ls xq.kk djosQ] mu xq.kkvksa dk tksM+ fudky fy;k tkrk gSA
(Σfdx)A

(iv) vUr esa] fuEu lw=k dk iz;ksx fd;k tkrk gSμ
Σfdx Σfdx
=X + A or =X + A
N Σf
A = dfYir ekè;] Σfdx = fopyuksa o vko`fÙk;ksa dh xq.kkvksa dk tksM+]
N = vko`fÙk;ksa dk tksM+]
mnkgj.k (Illustration) 2: fuEufyf[kr [kf.Mr Js.kh esa (i) 15 dks 'kwU; (vFkkZr~ dfYir&ekè;) lekUrj ekè;
fudkfy;s rFkk (ii) izR;{k jhfr }kjk ifj.kke dh tk¡p dhft,μ

vkdkj (X)% 20 19 18 17 16 15 14 13 12 11
vko`fÙk (f)% 1 2 4 8 11 10 7 4 2 1
gy (Solution) : ;gk¡ dfYir&ekè; 15 ekuk tk,xk D;ksafd iz'u esa fn;k gqvk gSA
izR;{k rFkk y?kq jhfr }kjk lekUrj ekè; dk ifjdyu\

vkdkj vko`fÙk y?kq jhfr izR;{k jhfr
A = 15 ls fopyu xq.kuiQy
(X) (f) (dx) (fdx) (fX)
20 1 + 5 + 5 20
19 2 + 4 + 8 38
18 4 + 3 + 12 72
17 8 + 2 + 16 136
16 11 + 1 + 11 176
15 10 0 0 150
14 7 –1 –7 98
13 4 –2 –8 52
12 2 –3 –6 24
11 1 –4 –4 11
Total N = 50 Σfdx = 27 ΣfX = 777

y?kq jhfr (Short-cut Method) izR;{k jhfr (Direct Method)

Mean or

= 15 + 0.54 = 15. 54 ∴ X = 15.54

(C) v[kf.Mr Js.kh esa eè;d dk ifjdyu (Mean in Continuous Series)

v[kf.Mr Js.kh esa lekUrj ekè; Bhd mlh izdkj fu/kZfjr fd;k tkrk gS ftl izdkj [kf.Mr Js.kh esa lw=k Hkh nksuksa
esa ,d leku gSA ijUrq vUrj osQoy bruk gS fd v[kf.Mr Js.kh esa igys oxks± osQ eè;&ewY; (mid-values) fudkys
tkrs gSa ftUgsa 'X' dgrs gSaA bl izdkj eè;&ewY; ysus ij v[kf.Mr Js.kh] [kf.Mr Js.kh dk :i ys ysrh gSA

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