Page 72 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV gSA¸
izks- VqVys osQ vuqlkj ¶cgqyd og ewY; gS ftlosQ ,dne vkl&ikl vko`fÙk ?kuRo vf/dre gksrk gSA¸

cgqyd dk fu/kZj.k (Location or Computation of The Mode)
I. O;fDrxr Js.kh esa cgqyd fu/kZj.k (Mode in individual observation)

lS¼kfUrd :i ls ,d O;fDrxr Js.kh esa cgqyd fu/kZj.k rd ugha gks ldrk tc rd mls [kf.Mr ;k v[kf.Mr
Js.kh esa u cny ysA O;fDrxr Js.kh esa cgqyd fudkyus dh rhu fof/;k¡ gSaμ
1. O;fDrxr Js.kh dks [kf.Mr Js.kh esa cny dj (Change in discrete series),
2. lrr~ ;k v[kf.Mr Js.kh (Continuous series) esa cny dj]
3. lekUrj ekè; ;k eè;dk dh lgk;rk ls cgqyd dk vuqekuA
1. O;fDrxr Js.kh dks [kf.Mr Js.kh esa cnyukμtc O;fDrxr Js.kh osQ vusd ewY; nks ;k nks ls vf/d ckj
ik;s tkrs gSa rks mUgsa vkjksgh Øe osQ vuqlkj j[kdj muosQ lkeus mudh vko`fÙk fy[k nsrs gSaA fiQj fujh{k.k }kjk
vfèkdre vko`fÙk okys ewY; dks pqu fy;k tkrk gS] ;gh cgqyd gksrk gSA

mnkgj.k (Illustration) 7: fuEu Js.kh dk cgqyd Kkr dhft;sμ
20, 22, 23, 20, 22, 24, 25, 21, 22, 23, 24, 22

gy (Solution) : fujh{k.k ls Li"V gS fd 22 okyk in lcls vf/d (5) ckj vk;k gSA
vr% 22 gh cgqyd in gksxkA fiQj bls [kf.Mr Js.kh esa cnyus ij Hkh ;gh ifj.kke gksxkμ
x : 20 21 22 23 24 25
y : 2 1 5 2 2 1
vr% cgqyd (mode) ;k z = 2
;fn nks ;k vf/d pj ewY;ksa dh vko`fÙk;k¡ vf/dre gksa rks cgqyd fu/kZj.k dfBu gks tkrk gSA ,slh fLFkfr
esa lead Js.kh esa mrus gh cgqyd gksaxs ftruh vf/dre vko`fÙk;k¡ gksaxhA ,slh leadekyk,¡ f}&cgqyd
(bi-modal), f=k&cgqyd (Tri-modal) ;k vusd cgqyd (multi-modal) Jsf.k;k¡ dgykrh gSaA

mnkgj.k (Illustration) 8: fuEu leadksa ls cgqyd ifjdfyr dhft,μ
Øekad : 1 2 3 4 5 6 7 8 9 10
vkdkj : 2 14 10 14 22 10 8 14 10 12
gy (Solution): fujh{k.k ls Li"V gS fd 14 vkSj 10 okys in rhu&rhu ckj vk;s gSa vr% bldk cgqyd
vfuf'pr vFkkZr~ vfuèkkZfjr gS vFkkZr~ ;g ,d f}&cgqyd Js.kh (bimodal series) gSA
2. lrr~ ;k v[kf.Mr Js.kh esa cnyukμtc Js.kh esa dksbZ Hkh O;fDrxr ewY; ,d ls vf/d ckj ugha ik;k
tkrk gS rks mls [kf.Mr Js.kh esa cnyuk O;FkZ gksxk D;ksafd lHkh ewY;ksa dh vko`fÙk leku gksus ij cgqyd fuèkkZj.k
djuk vlEHko gksrk gSA ,slh fLFkfr esa mls lrr~ vko`fÙk caVu osQ :i esa cnydj vf/dre vko`fÙk okyk
oxkZUrj Kkr dj ysuk pkfg,A fiQj bl cgqyd oxZ esa lw=k }kjk cgqyd ewY; Kkr fd;k tk ldrk gSA
3. lekUrj ekè; ,oa eè;dk dh lgk;rk ls cgqyd fu/kZj.kμ;fn fdlh O;fDrxr Js.kh esa eè;dk (M),

lekUrj ekè; (X) vkSj cgqyd rhuks gh Kkr djus gksa rks bu rhuksa osQ ikjLifjd lEcU/ ij vk/kfjr fuEu lw=k
}kjk gh cgqyd ewY; dk vuqeku yxkuk pkfg,μ
(X − Z) = 3(X − M) or Z = 3M – 2X
II. [kf.Mr Js.kh esa cgqyd fu/kZj.k (Mode in Discrete Series)

[kf.Mr Js.kh esa cgqyd fu/kZj.k dh nks jhfr;k¡ gSaμ(a) fujh{k.k jhfr] (b) lewgu jhfrA

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