Page 70 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV gksa rks rhljk eku fuEu lw=k }kjk Kkr fd;k tk ldrk gSμ
ΣX ΣfX ΣX ΣfX
X = or , ΣX or ΣfX = X × N, N = or
N N X X

mnkgj.k (Illustration) 6: ;fn fuEu vko`fÙk caVu dk lekUrj ekè; 67-45 gS rks vKkr vko`fÙk Kkr dhft,μ
ekDZl : 60-62 63-65 66-68 69-71 72-74
vko`fÙk: 15 54 – 81 24

gy (Solution): ekuk vKkr vko`fÙk gSμ
vKkr vko`fÙk fu/kZj.k (Locating the Missing Frequency)

ekDZl Mid-values vko`fÙk Total Size
X X f X×f
60–62 61 15 915
63–65 64 54 3456
66–68 67 f 67 f
69–71 70 81 5670
72–74 73 24 1752

Total N = 174 + f ΣfX = 11793 + 67 f
+
ΣfX 11793 67 f
X = or 67.45 =
N 174 + f
67.45 (174 + f) = 11793 + 67 f or 11736.3 + 67.45 f = 11793 + 67 f
67.45 f – 67 f = 11793 – 11736 or 0.45 f = 56.7 or f = 126

vr% vKkr vko`fÙk 126 gSA
lekUrj ekè; dh lhek,¡ (Limitations of Arithmetic Mean)

,d vkn'kZ ekè; gksus osQ ckotwn lekUrj ekè; fuEu nks"kksa ls xzflr gSμ
(1) pje ewY;ksa dk izHkko (Effect of Extreme Values)μ bl ekè; dk lcls cM+k nks"k pje&ewY;ksa
(vR;f/d cM+s ;k NksVs ewY;ksa) dks vf/d egÙo nsuk gSA mnkgj.kkFkZ] pkj deZpkfj;ksa osQ osru Øe'k% 1000]
250] 210] 180 #- dk lekUrj ekè; 410 gqvkA Li"V gS fd vosQys in&ewY; (1000) us vkSlr dks dkiQh
gn rd c<+k fn;k gS

(2) vokLrfod ekè; (Unrealistic Average)μ lekUrj ekè; dHkh&dHkh iw.kk±d u gksdj n'keyo ;k
fHkUu osQ :i esa vkrk gS tksfd bls vokLrfod cuk nsrk gSA mnkgj.kkFkZ] pkj ekrkvksa }kjk Øe'k% 3] 2] 1 o
4 cPpksa dks tUe fn;k x;k ftldk izfr ekrk vkSlr 2-5 vk;kA fu%lansg ;g ,d gkL;izn fu"d"kZ gSA
(3) vizfrfuf/Roμ lekUrj ekè; fdlh Js.kh dk ,d ,slk ewY; gks ldrk gS tks ml Js.kh esa u gksdj dksbZ
ckgj dk ewY; gksA mnkgj.kkFkZ] 6] 7 o 2 dk lekurj ekè; 5 gS tks bu rhuksa esa ls ,d Hkh ugha gSA ;gh dkj.k
gS fd ;g ekè; mfpr izfrfuf/Ro ugha dj ikrkA
(4) x.kuk laca/h tfVyrkμ fLFkfr laca/h ekè;ksa tSls Hkwf;"Bd o eè;dk dh vis{kk lekurj ekè; dh
x.kuk&fØ;k vf/d tfVy gSA izFke] ;g fujh{k.k }kjk ugha fudkyk tk ldrkA nwljk] ;fn Js.kh dk dksbZ ,d
ewY; Hkh vKkr gS rks lekUrj ekè; ugha fudy ik;sxk D;ksafd ;g Js.kh osQ lHkh ewY;ksa ij vk/kfjr gksrk gSa

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