, , , , , , , . .
6
, . . | 20 -40 | 40 -60 | 60 -80 | 80 -100 | 100 -120 |
() :
7
, . , | , f | , ´ = ( +) / 2 | ´ * f | ׀ ´ - ׀ | ׀ ´ - ׀ * f | (´ - )2 | (´ - )2 * f |
20 - 40 | 37, 98 | 455, 76 | 1442, 48 | 17309, 76 | |||
40 60 | 17, 98 | 323, 28 | |||||
60 80 | 2, 02 | 191, 9 | 4, 08 | 387, 6 | |||
80 100 | 22, 02 | 616,56 | 484, 88 | 13576, 64 | |||
100 - 120 | 42, 02 | 546, 26 | 1765, 68 | 22953, 84 | |||
- | - | 2709, 48 | 4020, 4 | 70 391, 84 |
, (´) (. ) (. 2).
(´) (fi) (. 3). :
= ∑(i * fi) / ∑ fi = 13460 / 198 = 67, 98 . . 1 .
, (´) () (. 4). , , .
, ׀ ´ - ׀ (fi) . 2709, 48. . 5.
(d) :
d = ∑ ׀ ´ - * ׀ fi / ∑fi = 2709, 48 / 198 = 13, 6842
. . 54, 2958 . . , , . , , (, 3,67 110 30).
(σ2) (σ), .
|
|
σ2 = ∑( ´ - )2 * fi / ∑fi =70 391, 84 / 198 = 355, 51 . .
σ = (∑( ´ - )2 * fi / ∑fi)1/2 = (355, 51)1/2 = 18, 85 . .
, 67, 98 . . .
(VR):
VR = R / * 100%
R = ´ - ´ = 120 20 = 100 . .
VR = R / * 100% = 100 / 67, 98 * 100 % = 147, 1%.
(Vd):
Vd = d / * 100% = 13, 6842 / 67, 98 * 100% = 20, 13%
(Vσ):
Vσ = σ / * 100% = 18, 85/ 67, 98 * 100% = 27, 73 %
. . 33%.
():
= 0 + i * (f f-1) / ((f f-1) + (f f+1)),
0 ( , 60 -80);
i (20 . .);
f (95);
f-1 , (50)
f+1 , (28).
= 60 + 20* ((95 50) / (95 28)) = 73, 43 . .
73, 43 . . 95 .
():
= 0 + i * (1/2 * ∑fi S 1) / f,
0 ( , 198 / 2 = 99, 60 -80 . . 12 + 50 + 95 = 157);
i (20 . .)
S 1 , (12 + 50 = 62);
f (95).
=60 + 20 * (99 62) / 95 = 67, 79 . .
67, 79 . .
, . ( ) . , , , .
, , . , . . .
8
, . . | , f | , ´ = ( +) / 2 | |
20 40 | |||
40 60 | |||
60 80 | |||
80 100 | |||
100 120 | |||
- | - |
|
|
. 2.
, , , .
. 3.
, , , , . 1 , :
9
, . | , . |
2000 | |
2000 2050 | |
2050 2100 | |
2100 2150 | |
2150 | |
, 2000 2150 .
1. () ( .) ( .) :
= . .
. . , , , . . . 1950 (2000 50), . 2200 (2150 +50).
= 2200 1950 = 250.
250.
2. , d., :
d = ∑(i .)*f / ∑ f,
i , ;
f .
. , (2075)
6.2.
10
, . | , . | |||||||
1i =( i+1 + i)/2 | 1i* f | (i.)= i - 2075 | (i .) *f | (i .)2 | (i .)2 * f | |||
1950 - 2000 | - 100 | -400 | ||||||
2000 2050 | - 50 | -750 | ||||||
2050 2100 | ||||||||
2100 2150 | ||||||||
2150 - 2200 | ||||||||
d= 2750/100 = 27,5
3. (σ2) , (i .)2
σ2 = ∑ (i .)2 / n-1
σ2 = 93500 / 4= 23375
4. (σ2) (σ)
σ = √ σ2 =√23375 = 152,89 .
, .
5. (ν) :
ν= σ/ *100% = 152,89 /2075*100% = 7,37%
6. :
μw ~ √(w*(1- w)/n) *(1- n/N),
w
100 , n, 90 . (15+55+20), 2000 2150 , (m),
w = m/ n=90/100=0,9
μw ~ √(0,9(1-0,9)/100)*(1-100/2000)= +0,029
μ=√ (σ2/ n)*(1- n/N)= 23375/100*0,95= +222,06
(+0,029) (+222,06 ) (p) ( 1).
0,997, t = 3,0 :
|
|
p = w +-t * μw=0,9+-3*0,029
. . 0.9-0,087=0,813 0.9+0,087=0,987
, 99 100 81,3% 98,7%.
,
1= -+ _ t * μ = 2075-+ 3*222,06
. . 1408,82 2741,18
, , 0,997 , 1408,82 2741,18 .
0,954, t = 2,0 :
p = w +-t * μw=0,9+-2*0,029
. . 0.9-0,058=0,842 0.9+0,058=0,958
, 99 100 84,2% 95,8%.
,
1= -+ _ t * μ = 2075-+ 2*222,06
. . 1630,88 2519,12
, , 0,954 , 1630,88 2519,12
1. .. . .: - . , 2008.
2. .. . .: , 2008.
3. : : / . .. ... .: , 2008.
4. : / . ... .: , 2007.
5. : / . ... .: -, 2006.
6. .. : . : - , 2006.
7. : / . ... .: -, 2008.