Page 293 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—20% vfojks/ dk ifj{k.k% bdkbZ ekin.M] le; mRØE;rk ijh{k.k] rRo mRØE;rk ijh{k.k] pØh; ijh{k.k

gy (Solution). uksV
fiQ'kj osQ vkn'kZ lwpdkad dk ifjdyu

Item 1990 1992 Product
p q p q p q p q p q p q
0 0 1 1 0 0 1 0 0 1 1 1
A 6 50 10 56 300 500 336 560
B 2 100 2 120 200 200 240 240
C 4 60 6 60 240 360 240 360
D 10 30 12 24 300 360 240 288
E 8 40 12 36 320 480 288 432
Total 1360 1900 1344 1880
Σp q Σp q Σp q Σp q
0 0 1 0 0 1 1 1

fiQ'kj dk vkn'kZ lwpdkad % lw=kμ
Σ 10 Σpq pq 1900 1880
11
P = × × 100 = × × 100
01 Σ 00 Σpq pq 1360 1344
0 1
= 1.397 × 1.399 × 100 = 1.954 × 100
= 1.398 × 100 ∴ P = 139.8
01
y?kqx.kd jhfr (Logrithms method) }kjk gy djus ijμ
1
Log P = [(log 1900 – log 1360) + (log 1880 – log 1344)] + log 100
01 2
1
= [(3.2788 + 3.1335) + (3.2742 – 3.1284)] + 2.0000
2
1
= [(0.1453 + 0.1458) + 2 or = Antilog 0.1455 + 2
2
= Antilog 2.1455 ∴ P = 139.8
01
le;&mRØkE;rk ijh{k.k (Time Reversal Test):

Σpq Σpq Σpq Σpq
P = 10 × 11 P = 00 × 01
01 Σpq Σpq 10 Σpq Σpq
10
00
01
11
Kkr ewY;ksa dks lw=k esa vkfn"V djus ijμ
1900 1880 1360 1344
P × P = × × × = 1 = 1
01 10 1360 1344 1900 1880
vr% fiQ'kj dk vkn'kZ lwpdkad bl ijh{k.k dks iwjk djrk gSA
fVIi.khμx.kuk&fØ;k dks ljy djus osQ fy, 100 dh xq.kk ugha dh tkrh gSA
rRo&mRØkE;rk ijh{k.k (Factor Reversal Test):
Σpq Σpq Σpq Σpq Σpq
P × Q = 10 × 11 × 01 × 11 = 11
01 01 Σpq Σpq Σpq Σpq Σpq
00
10
00
01
00
1900 1880 1344 1880 1880 1880 1880
= × × × = × = (Proved)
1360 1344 1360 1900 1360 1360 1360
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