Page 67 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

uksV

;fn oxZ&foLrkj leku gS rks ^y?kq jhfr* Js"B gS vkSj ;fn oxks± dk foLrkj vleku gS
rks ^izR;{k jhfr* mi;qDr gksxhA

lekUrj ekè; laca/h oqQN Lej.kh; ckrsa (Some Memorable Points Regarding
Arithmetic Mean)
(1) in&fopyu jhfr (Step Deviation Method)μ y?kq jhfr dks vkSj Hkh ljy cukus osQ fy;s in&fopyu
jhfr dk iz;ksx fd;k tk ldrk gS c'krZs fd Js.kh esa oxZ&foLrkj ^leku* gksA y?kq jhfr vkSj bl jhfr esa varj osQoy
bruk gS fd y?kq jhfr esa tks fopyu fy;s tkrs gSa mUgsa bl jhfr esa fdlh lekioÙkZd (common factor) ls Hkkx
nsdj laf{kIr cuk fy;k tkrk gSA bUgsa gh in&fopyu (d'x) dgrs gSaA lkekU;r% oxZ&foLrkj dks gh lekioÙkZd ekuk
tkrk gSA fiQj] in&fopyuksa dks mudh vko`fÙk;ksa ls xq.kk djosQ Σdf'x Kkr dj yrs gSaA var esa] lek;kstu dh n`f"V
ls Σdf'x esa lekioÙkZd (i) ls xq.kk dj nh tkrh gSA lw=k o mnkgj.k uhps nsf[k,A
y?kq jhfr in&fopyu jhfr

Σfdx Σfd' x
=X + A X = + A × i
N N
Σfd'x = in&fopyuksa rFkk vko`fÙk;ksa dh xq.kkvksa dk tksM+
i = lekioÙkZd oxZ&foLrkj
(2) lap;h vko`fÙk&forj.kμ dHkh&dHkh oxkZUrjksa dks lap;h vk/kj ij fn;k tkrk gSA ,slh fLFkfr esa lap;h
forj.k dks lekU; forj.k esa cny ysuk pkfg;sA
mnkgj.k (Illustration) 5: fuEu lkj.kh ls lekUrj ekè; fudkfy,
izkIrkad: 10 20 30 40 50 60 70 80
vo`fÙk : 25 40 60 75 95 125 190 240

gy (Solution): loZizFke lap;h vko`fÙk forj.k dks lkekU; vko`fÙk forj.k esa cnyk tk;sxkμ
lekUrj ekè; dk ifjdyu (in&fopyu jhfr)

izkIrkad eè;&fcanq vko`fÙk in&fopyu xq.kuiQy
X M.P. f d'x = X – 45/10 f × d'x
0 – 10 5 25 — 4 — 100
10 – 20 15 15 — 3 — 45
20 – 30 25 20 — 2 — 40
30 – 40 35 15 — 1 — 15
40 – 50 45 20 0 0
50 – 60 55 30 + 1 + 30
60 – 70 65 65 + 2 + 130
70 – 80 75 50 + 3 + 150
N = 240 Σfdx = 110

Σfd' x 110
Mean Marks or =X + A × = i 45+ × 10
N 240
= 45 + 4.58 ∴ ekè; izkIrkad = 49.58

LOVELY PROFESSIONAL UNIVERSITY 61