Page 80 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV 5-3 eè;dk osQ vuqiz;ksx (Application of Median)

eè;dk Hkh cgqyd dh rjg fLFkfr laca/h ,d ekè; gSA eè;dk] ,d Øec¼ lead&ekyk dk osQUnzh; ;k
eè;&ewY; gksrk gS vFkkZr~ mls nks cjkcj Hkkxksa esa foHkkftr djrk gSA izks- dkSuj osQ vuqlkj] ¶eè;dk leadJs.kh
dk og pkj&ewY; gS tks lewg dks nks cjkcj Hkkxksa esa bl izdkj ckaVrk gS fd ,d Hkkx osQ lHkh ewY; eè;dk
ls de (vFkkZr~ NksVs) rFkk nwljs Hkkx osQ lHkh ewY; eè;dk ls vf/d (vFkkZr~ cM+s) gksaA mnkgj.kkFkZ] ;fn 5
Nk=kksa osQ izkIrkad Øe'k% 2] 5] 6] 9] 14 gksa rks mudk eè;dk 6 gksxk D;ksafd ;g rhljs Øe dk vad Js.kh
osQ fcYoqQy eè; esa fLFkr gS vkSj blls igys osQ nksuksa vad (2] 5) blls NksVs gSa rFkk ckn osQ nksuksa vad (9]
14) blls cM+s gSaA

eè;dk dk fu/kZj.k (Computation of Median)
O;fDrxr Js.kh esa eè;dk fu/kZj.k (Median in Individual Series)μO;fDrxr Js.kh esa eè;dk Kkr osQ
fy, fuEu fØ;k,¡ dh tkrh gSaμ

(a) lcls igys in&ewY;ksa dks vkjksgh ;k vojksgh Øe esa vuqfoU;kflr fd;k tkrk gSA nksuksa Øeksa esa osQUnz&fcUnq
,d gh gksrk gSA ewY;ksa dh Øe la[;k,¡ Hkh lkFk&lkFk fy[k nsuh pkfg,A
(b) Øec¼ djus osQ ckn fuEu lw=k dk iz;ksx djuk pkfg,μ
M = Size of G F H N + I 1 K J th item M → Median (eè;dk)
2

N → Number of items (inksa dh la[;k)
bl lw=k osQ }kjk gesa eè;dk ewY; Kkr ugha gksrk cfYd eè;dk la[;k dk irk py tkrk gS] blh Øe la[;k
dk in ewY; gh okLro es eè;dk ewY; gksrk gSA

le in la[;k okyh Js.kh esa eè;dk fu/kZj.k
;fn O;fDrxr Js.kh esa le in la[;k gksrh gS vFkkZr~ 2 ls foHkkT; gS_ tSlsμN = 8 ;k N = 12 rks lw=k }kjk Kkr
gksus okyh Øe la[;k iw.kk±d ugha gksxh cfYd 4.5 ;k 6.5 gksxhA ,sls esa Øe la[;k dk fu/kZj.k djus osQ fy,
mlosQ nksuksa vksj dh nks iw.kZ Øe la[;kvksa osQ ewY;ksa dks tksM+dj 2 ls foHkkftr dj fn;k tkrk gSA ;gh eè;dk
ewY; gksrk gSA
Value of 4th item + Size of 5th item
Size of 4.5th item =
2
23 + 29 52
= = = 26
2 2
Median marks (M) = 26

[kf.Mr Js.kh ;k fofPNUu Js.kh (Discrete series) esa eè;dk fu/kZj.kμ[kf.Mr Js.kh esa eè;dk Kkr djus
osQ fy, fuEu fØ;k,¡ dh tkrh gSaμ

1- lcls igys lap;h vko`fÙk;k¡ Kkr dh tkrh gSa vkSj lap;h vko`fÙk Js.kh esa cny fy;k tkrk gSA
2- blosQ ckn fuEu lw=k }kjk eè;dk dh Øe la[;k Kkr dj yh tkrh gSμ
M = Size of G F H N + I 1 K J th item N vko`fÙk dk ;ksx
2

3- eè;dk lkbt ;k Øe la[;k dk ewY; lap;h vko`fÙk dh lgk;rk ls Kkr dj fy;k tkrk gSA ftl lap;h
vko`fÙk esa ;g Øe la[;k izFke ckj 'kkfey gksrh gS mldk ewY; gh eè;dk gksrh gSA

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