D Z/Z = [(D X)2 + (D Y)2]1/2/(X + Y)(29)
X Y.
, , . , , . . x 1, x 2,..., n , S 2. y,
y = (1/ n)× Axi = x 1/ n + x 2/ n +... + n / n.
Sy 2 (26)
Sy 2 = S 2/ n 2 + S 2/ n 2 +... + S 2/ n 2 = nS 2/ n 2 = S 2/ n (30)
y, , xi,
Sy = S < x > = S / n 1/2. (31)
, .
. , , 2 , ; 3 , 9 , , , 100 .
, , . , n , . , .
.
, 0.05 , - 100 , .
M SM = [1S100 S i2]1/2;.
, 100, SM = (100)1/2× S = 10× S = 10´0.05 = 0.5 .
, , 1000 , , 320 0.5 , 50 1 , 1.5 .
nS S < x >.
, , .
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, , nS s, n .
.
R, , .4.
<R> = S Ri /10 = 274.7, 10S 1.6, nS < R > = 1.6/101/2 0.5.
4.
R |
, SR 0.5 , , , 0.2%. 10 S 1.6 , 0.6%.
, , . , , , .1V, .
[9]) . R :
R = 274.7 (0.5).
6.
, k . n 1, - n 2 .., k - - nk; s, i (26)[10])
s i = s/(ni)1/2.
, , , .
, , . . , , ,
pi = k×ni.
ni (16),
pi = k× s2/s i 2
, k s2 = ,
pi = K/ s i 2.
, , s i, pi,
pi = B/ s i 2.
B . , pi, . , s i , , , , , , , ..
, , , , - . , 10 (s i s k ), , .
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xi pi, , , < x >:
< x > = 1S npixi /1S npi. (32)
, p 1 = p 2 =... = pn, (32) (3).
< x > , .
nS < x > = {[1S npi (< x > xi)2]/[(n 1)×1S npi ]}1/2 (33)
, . ( . . 67).
7.
. II xi, , , xi D x. , , x < x > . .IV, , , s s< x >, s xi / n 1/2.
e, . II,
e = D x /s< x > = D x × n 1/2/s. (34)
, , s. , , . , , , s. , , . nS, , n (2 S, 3 S, 4 S,..., nS , (16) , , .. ). , s, .II , () a.
, . , s nS, , , n.
( 25¸30 ) , s2 nS2 .
nS 2 n D x .
, (34) s n S2 . , D x
D x = t a, n × nS / n 1/2, (35)
t a, n = D x × n 1/2/ nS. (36)
, t a, n , e: , , , nS, .
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t a, n , , a . III, .
.III .II, , n t a, n e. , n nS s.
, (21)
P ( [<x> t a, n nS / n 1/2] < x < [< x > + t a, n nS / n 1/2] ) = a. (37)
. III, .
. III. 5 31.2. , 5 , 0.24. , 0.2, 31.0< x < 31.4,
t a,5 , (36),
t a,5 = 0.251/2/0.24 = 1.86.
. III n = 5 a = 0.8 t 0.8,5 = 1.5, a = 0.9 t 0.9,5 = 2.1.
, , 0.8 0.9. , , .
Da/(a2 a1) = (t a,n t 0.8, n )/(t0.8,n t 0.9,n),
Da = 0.1×(0.36/0.6) = 0.06, a = a1 +Da = 0.8 + 0.06 = 0.86.
, 0.86.
, 10 0.24 31.0¸31.4. (36)
t a,10 = 0.2×101/2/0.24 2.6.
. III ,
t a,10 = 2.3 a = 0.95
t a,10 = 2.8 a = 0.98.
Da = 0.3×0.03/0.5 0.02.
a = 0.97.
8.
. , ( ) .
, ?
, - , , . . < x > S:
<x >1, < x >2,..., < x > n S 1, S 2,..., Sn.
, ? . . , , . , , , , 0.05, 0.01 0.001, .
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, , , . , , , . , (. . 31).
, .
, . S , , , n , S , , , n.
, , , , n nS s .
, s,
s nS s/[2×(n 1)]1/2. (38)
s S n S, nS n ; , n, 30, n.
(38) , n = 25 s25S = s/7, s 7. n = 50 s 10.
s .
c2, :
c2 = (n 1) nS 2/s2.
c2-, .12.
c2 , n. n , (38). s , .
s , c2 -.
(39)
s2 = [(n 1)/c2] nS 2 = g2× nS 2. (40)
.III g1 g2
P (g1× n S < s) = a1, P (g2× nS > s) = a2.
c2 - , , , . ,
a1 = a2×g1 ¹ 1/g2.