1
1. :
- , 4-5 ( ) ;
- . ;
- ( );
- :
(, , Me);
(R, );
2. .
3. , , , . .
4. , () (η). .
- ;
- ; - ; - i- .
- ;
1
-
1 | 2 | |
(. .) | ( , %) | |
38,1 | ||
41,9 | ||
46,2 | ||
30,9 | ||
30,4 | ||
37,4 | ||
30,6 | ||
43,7 | ||
42,1 | ||
56,5 | ||
32,5 | ||
30,2 | ||
49,2 | ||
41,3 | ||
52,0 | ||
36,7 | ||
30,9 | ||
37,0 | ||
76,1 | ||
35,8 |
. . , , ; ; .
:
.
-, nj | ∑X | Xcp = ∑Xj / nj | ∑Y | Ycp = ∑Yj / nj | ||
352 - 650 | 1,2,3,4,5,6,7,8,9,10 | 467.7 | 351.4 | 35.14 | ||
650 - 948 | 11,12,13,14,15 | 755.8 | 206.4 | 41.28 | ||
948 - 1246 | 16,17 | 82.9 | 41.45 | |||
1246 - 1544 | ||||||
1544 - 1842 | 18,19,20 | 1762.33 | 178.8 | 59.6 | ||
789,15 | 819.5 | 40,975 |
|
|
4 , , .
, . .
.
-, nj | ∑X | Xcp = ∑Xj / nj | ∑Y | Ycp = ∑Yj / nj | ||
352 - 724.5 | 1,2,3,4,5,6,7,8,9,10,11,12 | 500.83 | 430.9 | 35.91 | ||
724.5 - 1097 | 13,14,15,16,17 | 897.2 | 209.8 | 41.96 | ||
1097 - 1469.5 | ||||||
1469.5 1842 | 18,19,20 | 1762.33 | 178.8 | 59.6 | ||
789,15 | 819.5 | 40,975 |
. : .
1. .
:
2. - ( ).
: 352 - 650 (1,2,3,4,5,6,7,8,9,10)
yj | (yj - y)2 | |
30.6 | (30.6 - 35.14)2 | 20.61 |
32.5 | (32.5 - 35.14)2 | 6.97 |
38.1 | (38.1 - 35.14)2 | 8.76 |
30.2 | (30.2 - 35.14)2 | 24.4 |
(37 - 35.14)2 | 3.46 | |
30.9 | (30.9 - 35.14)2 | 17.98 |
30.4 | (30.4 - 35.14)2 | 22.47 |
36.7 | (36.7 - 35.14)2 | 2.43 |
35.8 | (35.8 - 35.14)2 | 0.44 |
49.2 | (49.2 - 35.14)2 | 197.68 |
305.2 |
() 1- :
: 650 - 948 (11,12,13,14,15)
yj | (yj - y)2 | |
37.4 | (37.4 - 41.28)2 | 15.05 |
42.1 | (42.1 - 41.28)2 | 0.67 |
43.7 | (43.7 - 41.28)2 | 5.86 |
41.9 | (41.9 - 41.28)2 | 0.38 |
41.3 | (41.3 - 41.28)2 | 0.0004 |
21.97 |
() 2- :
: 948 - 1246 (16,17)
yj | (yj - y)2 | |
(52 - 41.45)2 | 111.3 | |
30.9 | (30.9 - 41.45)2 | 111.3 |
222.61 |
() 3- :
: 1246 - 1544 ()
yj | (yj - y)2 | |
() 4- :
: 1544 - 1842 (18,19,20)
yj | (yj - y)2 | |
56.5 | (56.5 - 59.6)2 | 9.61 |
76.1 | (76.1 - 59.6)2 | 272.25 |
46.2 | (46.2 - 59.6)2 | 179.56 |
461.42 |
() 5- :
3. :
:
4. ,
δ2 = ((35.14-40.98)2*10 + (41.28-40.98)2*5 + (41.45-40.98)2*2 + (0-40.98)2* + (59.6-40.98)2*3)/20 = 69.1
|
|
, :
σ2 = 50.56 + 69.1 = 119.66
:
yi | (yi - y)2 | |
30.6 | (30.6 - 40.98)2 | 107.64 |
32.5 | (32.5 - 40.98)2 | 71.83 |
38.1 | (38.1 - 40.98)2 | 8.27 |
30.2 | (30.2 - 40.98)2 | 116.1 |
(37 - 40.98)2 | 15.8 | |
30.9 | (30.9 - 40.98)2 | 101.51 |
30.4 | (30.4 - 40.98)2 | 111.83 |
36.7 | (36.7 - 40.98)2 | 18.28 |
35.8 | (35.8 - 40.98)2 | 26.78 |
49.2 | (49.2 - 40.98)2 | 67.65 |
37.4 | (37.4 - 40.98)2 | 12.78 |
42.1 | (42.1 - 40.98)2 | 1.27 |
43.7 | (43.7 - 40.98)2 | 7.43 |
41.9 | (41.9 - 40.98)2 | 0.86 |
41.3 | (41.3 - 40.98)2 | 0.11 |
(52 - 40.98)2 | 121.55 | |
30.9 | (30.9 - 40.98)2 | 101.51 |
56.5 | (56.5 - 40.98)2 | 241.03 |
76.1 | (76.1 - 40.98)2 | 1233.77 |
46.2 | (46.2 - 40.98)2 | 27.3 |
2393.26 |
, . :
:
(). :
0.1 < η < 0.3: ;
0.3 < η < 0.5: ;
0.5 < η < 0.7: ;
0.7 < η < 0.9: ;
0.9 < η < 1: ;
Y X
.
:
, 57.75% , 42.25% .
- .
x0 ; h ; f2 , ; f1 ; f3 .
352, .
550.67
: , .
, . , . 352 - 650, .. S, ( , S ).
, 50% 650
.
.
- .
R = Xmax - Xmin
R = 1842 - 352 = 1490
- , .
, 320.35
- ( , .. ).
( ).
813.9 , 415.87
.
: , , .
- : , .
|
|
v>30%, v<70%, .
- .
2
, .
:
1. , , ( ), 1 % ;
2. , , ;
3. , ( ). .
2
-
1- | 2- | 3- | 4- | 5- | 6- | |
, . . |
, , ( ), 1 %
.
( , ), .
, .
:
1)
)
)
: .
2)
)
)
3) , , ..:
)
)
4)
)
,
)
5) , :
= * 100
= 100
)
)
1)
: n .
2)
:
3)
y | ||||||||
100,00% | ||||||||
1,286 | 1,286 | 128,6% | 128,6% | 0,286 | 0,286 | |||
1,506 | 1,171 | 150,6% | 117,1% | 0,506 | 0,171 | |||
-27 | 1,496 | 0,993 | 149,6% | 99,3% | 0,496 | -0,007 | ||
2,138 | 1,429 | 213,8% | 142,9% | 1,138 | 0,429 | |||
2,861 | 1,338 | 286,1% | 133,8% | 1,861 | 0,338 |
, 123,4%
, ( ). .
. . : .
T | y | ys | |
- | - | ||
3336.33 | (2639 + 3395 + 3975)/3 | ||
3772.67 | (3395 + 3975 + 3948)/3 | ||
4521.33 | (3975 + 3948 + 5641)/3 | ||
5712.67 | (3948 + 5641 + 7549)/3 | ||
4396.67 |
|
|
y = bt + a
1. .
:
a0n + a1∑t = ∑y
a0∑t + a1∑t2 = ∑yt
t | y | t2 | y2 | ty |
:
7a0 + 28a1 = 27147
21a0 + 140a1 = 110645
0
a0 = 73.46, a1 = 3584.29
:
y = 73.46 t + 3584.29
a b βi, .
b = 73.46 ( ) t . t 1 , y 73.46.
3
(. .) (. .) ( 3) :
, .
. .
3
1 | 2 | |||||||
, .. | , . | , .. | , . | |||||
. | . | . | . | . | . | . | . | |
3,3 | 3,5 | 2,9 | 2,6 |
1 | ||||
, .. | , . | |||
. | . | . | . | |
(1) | 3,3 | 3,5 | ||
( 2) | 2,9 | 2,6 |