Page 352 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV Illustration 7. fuEu vk¡dM+ksa dks U;wure oxZ jhfr }kjk ljy js[kh; miufr iznku dhft, rFkk o"kZ 1990 osQ fy,
fcØh dh ek=kk dk vuqeku yxkb,μ
o"kZ : 1960 1965 1970 1975 1980 1985
foØh : 12 15 17 22 24 30
gy (Solution): bl iz'u esa nks fof'k"Vrk,¡ gSaA izFke] le;&bdkb;ksa dh la[;k ;qXe (even) gSA vr%
ewy&fcUnq (origin) chp osQ nks o"kks± (1970 rFkk 1975) dk eè;&o"kZ vFkkZr~ 1972.5 gksxkA nwljk] le;&bdkb;ksa
esa 5 o"kZ dk le; vUrjky (time-interval) gSA vr% o"kZ 1960 dk fopyu (X) fuEuor~ gksxk vFkkZr~μ
.
t − 1972 5 1960 − 1972 5 − 12 5
.
.
X = = = = – 5
/
12 × (interval) 05 × 5 25
.
.
blh izdkj vxys fopyu (X) Øe'k% – 3, – 1, + 1, + 3, + 5 vk,¡xsA
U;wure oxZ y?kq&jhfr }kjk ljy&js[kh; miufr fuèkkZj.k
t − 1972.5
Year Sale Lakh Rs. Squares X × Y Trend Values
2.5
Product
X Y X X 2 XY a + bX = Y c
1960 12 – 5 25 – 60 20 + (1.74 × – 5) = 11.30
1965 15 – 3 9 – 45 20 + (1.74 × – 3) = 14.78
1970 17 – 1 1 – 17 20 + (1.74 × – 1) = 18.26
1975 22 + 1 1 + 22 20 + (1.74 × 1) = 21.74
1980 24 + 3 9 – 72 20 + (1.74 × 3) = 25.22
1985 30 + 5 25 + 150 20 + (1.74 × 5) = 28.70
N = 6 ΣY = 120 0 70 + 122 120.00

pw¡fd ΣX = 0, vr% ‘a’ rFkk ‘b’ dk eku y?kq&jhfr }kjk Kkr fd;k tk,xkμ
ΣY 120 ΣXY 122
a = = = 20 b = = = 1.74
N 6 ΣX 2 70
vr% miufr js[kk (trend line) : Y = 20 + 1.74X
o"kZ 1990 osQ fy, iwokZuqekfur fcØhμ1990 osQ fy, X = + 7
∴ Y = 20 + (1.74 × 7) = 32.18 yk[k #-

24-5 vYidkyhu mPpkopuksa dh eki (Measurement of Short-Time
Oscillations)

dky&ekykvksa ij nh?kZdkyhu izo`fÙk vkSj vYidkyhu mPpkopuksa nksuksa dk gh lkewfgd izHkko iM+rk gSA
nh?kZdkyhu mPpkopuksa dk eki miufr (Trend) dh lgk;rk ls fd;k tkrk gSA py ekè; ;k U;wure oxZ jhfr
}kjk x.kuk fd;s x;s izo`fÙk ewY;ksa dks ewy leadksa esa ls fujflr dj fn;k tkrk gS rks vYidkyhu mPpkopu
'ks"k jg tkrs gSaA bu 'ks"kksa esa vYidkyhu mPpkopuksa vkrZo] pØh; o nSo ifjorZuksa dks 'kkfey djrs gSaA
mnkgj.k (Illustration) 8: fuEu vk¡dM+ksa ls vYidkyhu Kkr dhft, rFkk mudks xzkiQ isij ij iznf'kZr
dhft,%

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