Page 79 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

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

5. Js.kh ;k oxkZUrjksa dk vojksgh Øe (Descending Order of the series)μ;fn Js.kh vkjksgh osQ LFkku ij uksV
vojksgh Øe esa nh xbZ gS vFkkZr~ Åij ls uhps dh vksj ?kVrh gqbZ gS rks ge lw=k dk nks izdkj ls iz;ksx dj ldrs
gSaμ
(a) lkekU; lw=k dk iz;ksxμlkekU; lw=k dks iz;ksx djrs le; f dk eku cgqyd oxZ ls fupys oxZ dh
0
vko`fÙk gksxh ,oa f cgqyd oxZ ls mPprj oxZ dh vko`fÙk ekuh tk,xhA
2
(b) la'kksf/r lw=k dk iz;ksxμvojksgh oxkZUrj esa lkekU; lw=k esa FkksM+k ifjorZu djrs gSaA blesa (l +) osQ
1
LFkku ij (l –) dk iz;ksx djrs gSa vFkkZr~
2
vkjksgh oxkZUrj vojksgh oxkZUrj
f − f f − f
Z = l + f 2 1 − 1 f − 0 0 f 2 × i Z = l − f 2 1 1 − f − 0 0 f 2 × i
2
1
6. tc eè; ewY; fn;s x;s gksa (When mid-values are given)μdHkh&dHkh oxkZUrjksa osQ LFkku ij muosQ eè;
ewY; fn;s gksrs gSa D;ksafd v[kf.Mr Js.kh esa cgqyd Kkr djus osQ fy, Åijh ,oa fupyh nksuksa lhekvksa dh
vko';drk gksrh gSA vr% fuEu lw=k }kjk oxkZUrjksa dh Åijh ,oa fupyh lhek,¡ Kkr dj ysrs gSaμ
i i
l = M.V = 2 l = M.V + 2
2
1
7. vleku oxkZUrj okyh Js.kh (Series with unequal class intervals)μ;fn Js.kh esa oxZ foLrkj vleku gS
rks iz'u gy djus ls iwoZ mls leku dj ysuk pkfg, D;ksafd cgqyd dk lw=k ^leku oxkZUrj* dh ekU;rk ij
vk/kfjr gSA

;fn fdlh lrr~ vko`fÙk Js.kh dk cgqyd ,oa oqQy vko`fÙk;ksa dk ;ksx Kkr gks rks oqQN
vKkr vko`fÙk;ksa dk fu/kZj.k lw=k }kjk fd;k tk ldrk gSA

mnkgj.k (Illustration) 15: uhps fn;s viw.kZ caVu esa vKkr vko`fÙk dk eku Kkr dhft, ;fn bldk cgqyd
35 gSμ
oxZ vUrjky 0—10 10—20 20—30 30—40 40—50 50—60 60—70

vko`fÙk 10 12 14 20 — 12 10
gy (Solution): Z = 35, vr% cgqyd oxZ 30—40 gS vkSj vKkr vko`fÙk mlosQ ckn okys oxZ dh vFkkZr~ f 2
gSA
Z = 35, l = 30, f = 14, f = 20, i = 10, f = ?
2
1
1
0
f − f 20 − 14
i
Z= l + 1 0 ×= 30 + × 10
1
f 2 1 − f − 0 f 2 2 × 20 − 14 − f 2
6 × 10 60
35 = 30 + ;k 35 – 30 = ;k 5(26 – f ) = 60
26 − f 2 26 − f 2 2
130 – 5f = 60 ;k 5f = 130 – 60 = 70
2
2
70
∴ f = 5 = 14
2
vr% caVu dh vKkr vko`fÙk 14 gksxhA
LOVELY PROFESSIONAL UNIVERSITY 73