1.1− ( 2-3-9-15)
d, c | h, | d, c | h, | d, c | h, | d, c | h, | d, c | h, | d, c | h, | d, c | h, | d, c | h, |
16,5 | 20,8 | 30,0 | 24,2 | 21,5 | 20,0 | 26,5 | 25,5 | 22,0 | 22,8 | 26,1 | 23,0 | 23,5 | 22,6 | 17,5 | 20,0 |
22,0 | 22,2 | 24,3 | 23,8 | 10,5 | 12,0 | 20,0 | 20,5 | 23,0 | 22,8 | 27,0 | 21,0 | 30,0 | 25,7 | 23,0 | 24,1 |
28,5 | 24,1 | 23,0 | 23,0 | 24,5 | 25,3 | 22,0 | 19,7 | 25,0 | 24,5 | 24,1 | 20,0 | 16,5 | 20,8 | 26,4 | 24,7 |
15,0 | 18,9 | 22,7 | 22,1 | 10,5 | 15,0 | 17,0 | 18,8 | 22,0 | 21,8 | 18,0 | 16,0 | 30,0 | 24,2 | 18,0 | 19,0 |
21,1 | 22,1 | 22,3 | 23,4 | 30,0 | 25,0 | 19,0 | 17,8 | 25,0 | 20,0 | 22,5 | 19,1 | 21,5 | 20,0 | 22,5 | 23,7 |
21,0 | 21,8 | 25,0 | 24,0 | 22,0 | 23,5 | 17,5 | 20,0 | 16,4 | 17,0 | 21,2 | 22,2 | 26,5 | 25,5 | 24,0 | 23,0 |
23,0 | 24,1 | 26,4 | 24,7 | 18,0 | 19,0 | 22,5 | 23,7 | 22,7 | 22,0 | 24,0 | 18,0 | 22,0 | 22,2 | 28,5 | 24,0 |
24,0 | 23,0 | 28,5 | 24,0 | 22,0 | 22,5 | 23,0 | 23,5 | 27,5 | 24,9 | 13,0 | 14,7 | 24,3 | 23,8 | 22,0 | 22,0 |
16,0 | 19,4 | 32,0 | 25,0 | 24,0 | 22,5 | 18,0 | 20,3 | 25,0 | 24,0 | 11,5 | 14,0 | 10,5 | 12,0 | 23,0 | 23,5 |
21,8 | 21,6 | 27,0 | 24,0 | 23,5 | 23,0 | 28,0 | 23,1 | 13,0 | 16,4 | 13,0 | 15,7 | 20,0 | 20,5 | 16,0 | 19,4 |
30,0 | 25,5 | 21,5 | 23,0 | 22,0 | 21,0 | 24,5 | 24,2 | 24,0 | 21,8 | 35,0 | 22,0 | 28,5 | 24,1 | 32,0 | 25,0 |
36,0 | 26,5 | 31,0 | 25,0 | 27,5 | 24,5 | 13,0 | 18,7 | 12,5 | 14,0 | 22,3 | 22,4 | 23,0 | 23,0 | 24,0 | 22,5 |
19,0 | 20,0 | 21,5 | 23,9 | 30,5 | 27,5 | 27,0 | 24,0 | 10,5 | 15,0 | 20,0 | 20,0 | 24,5 | 25,3 | 18,0 | 20,3 |
24,0 | 25,4 | 19,0 | 18,7 | 20,5 | 19,8 | 20,0 | 21,6 | 24,0 | 21,8 | 19,0 | 20,4 | 22,0 | 19,7 | 21,8 | 21,6 |
36,0 | 26,0 | 18,0 | 16,7 | 32,0 | 27,0 | 21,5 | 22,4 | 20,0 | 21,0 | 19,5 | 18,0 | 15,0 | 18,9 | 27,0 | 24,0 |
21,0 | 19,0 | 30,0 | 25,0 | 11,0 | 12,0 | 14,0 | 18,6 | 19,0 | 20,5 | 10,0 | 11,4 | 22,7 | 22,1 | 23,5 | 23,0 |
19,0 | 19,5 | 33,5 | 26,0 | 26,0 | 23,4 | 16,0 | 18,9 | 20,0 | 19,0 | 12,5 | 14,0 | 17,0 | 18,8 | 30,0 | 25,5 |
19,5 | 17,7 | 29,0 | 24,2 | 21,5 | 22,5 | 28,0 | 23,0 | 20,0 | 20,2 | 30,0 | 25,0 | 21,2 | 22,1 | 21,5 | 22,0 |
21,5 | 22,0 | 32,0 | 25,3 | 24,5 | 24,2 | 18,0 | 17,2 | 17,0 | 18,7 | 29,5 | 25,3 | 22,3 | 22,4 | 22,0 | 21,0 |
28,5 | 27,0 | 17,5 | 19,7 | 36,0 | 29,5 | 24,0 | 21,8 | 29,5 | 26,4 | 13,0 | 15,5 | 30,0 | 25,0 | 24,5 | 24,2 |
29,0 | 23,4 | 10,0 | 10,4 | 25,5 | 22,3 | 19,0 | 18,3 | 20,5 | 20,1 | 15,0 | 16,0 | 19,0 | 17,8 | 36,0 | 26,5 |
20,3 | 21,8 | 20,0 | 21,3 | 21,0 | 20,6 | 28,5 | 26,0 | 17,5 | 21,0 | 8,0 | 7,8 | 21,0 | 21,8 | 31,0 | 25,0 |
24,5 | 22,4 | 24,5 | 22,0 | 22,0 | 26,0 | 17,5 | 18,7 | 27,1 | 22,4 | 22,0 | 20,1 | 25,0 | 24,0 | 27,5 | 24,0 |
18,0 | 18,5 | 12,5 | 13,5 | 30,0 | 26,0 | 22,5 | 22,5 | 26,0 | 23,3 | 19,0 | 17,8 | 22,0 | 22,5 | 13,0 | 18,7 |
15,0 | 18,3 | 23,0 | 22,5 | 13,0 | 14,5 | 22,0 | 23,8 | 15,0 | 16,1 | 28,0 | 24,5 | 10,5 | 15,0 | 28,0 | 23,1 |
. .
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i = (xmax − xmin) / k (1.1)
dmin = 8,0 .;
dmax = 36,0 .;
hmin = 7,8 .;
hmax = 29,5 .
id = (36,0 − 8,0) / 12= 2,33 ≈ 2 .
ih = (29,5 − 7,8) / 12 = 1,81 ≈ 2 .
1.2 −
, . | |||
8,0- 9,9 | 8,0- | . | |
10,0- 11,9 | 10,0- | ||
12,0- 13,9 | 12,0- | ||
14,0- 15,9 | 14,0- | ||
16,0- 17,9 | 16,0- | :: | |
18,0- 19,9 | 18,0- | ||
20,0- 21,9 | 20,0- | ||
22,0- 23,9 | 22,0- | ||
24,0- 25,9 | 24,0- | ||
26,0- 27,9 | 26,0- | ||
28,0- 29,9 | 28,0- | :: | |
30,0- 31,9 | 30,0- | :. | |
32,0- 33,9 | 32,0- | ||
34,0- 35,9 | 34,0- | . | |
36,0- 37,9 | 36,0- | :: | |
− |
1.3 −
, . | |||
7,0- 8,9 | 7,0- | . | |
9,0- 10,9 | 9,0- | . | |
11,0- 12,9 | 11,0- | :: | |
13,0- 14,9 | 13,0- | ||
15,0- 16,9 | 15,0- | ||
17,0- 18,9 | 17,0- | : |
1.3
19,0- 20,9 | 19,0- | : | |
21,0- 22,9 | 21,0- | ||
23,0- 24,9 | 23,0- | ||
25,0- 26,9 | 25,0- | ||
27,0- 28,9 | 27,0- | :. | |
29,0- 30,9 | 29,0- | . | |
− |
1.4 −
, | 9,0 | 11,0 | 13,0 | 15,0 | 17,0 | 19,0 | 21,0 | 23,0 | 25,0 | 27,0 | 29,0 | 31,0 | 33,0 | 35,0 | 37,0 | |
, | ||||||||||||||||
, % | 0,5 | 4,5 | 5,0 | 3,0 | 7,0 | 9,5 | 14,0 | 18,0 | 12,5 | 7,5 | 7,0 | 6,5 | 2,5 | 0,5 | 2,0 |
1.5 −
, | 8,0 | 10,0 | 12,0 | 14,0 | 16,0 | 18,0 | 20,0 | 22,0 | 24,0 | 26,0 | 28,0 | 30,0 | |
, . | |||||||||||||
, % | 0,5 | 0,5 | 2,0 | 3,0 | 5,0 | 11,0 | 16,0 | 22,5 | 24,5 | 13,0 | 1,5 | 0,5 |
1.6 −
, . | , . | ||||||||||||
7,0- 8,9 | 9,0- 10,9 | 11,0- 12,9 | 13,0- 14,9 | 15,0- 16,9 | 17,0- 18,9 | 19,0- 20,9 | 21,0- 22,9 | 23,0- 24,9 | 25,0- 26,9 | 27,0- 28,9 | 29,0- 30,9 | ||
8,0- 9,9 | |||||||||||||
10,0- 11,9 | |||||||||||||
12,0- 13,9 | |||||||||||||
14,0- 15,9 | |||||||||||||
16,0- 17,9 | |||||||||||||
18,0- 19,9 | |||||||||||||
20,0- 21,9 | |||||||||||||
22,0- 23,9 | |||||||||||||
24,0- 25,9 | |||||||||||||
26,0- 27,9 | |||||||||||||
28,0- 29,9 | |||||||||||||
30,0- 31,9 | |||||||||||||
32,0- 33,9 | |||||||||||||
34,0- 35,9 | |||||||||||||
36,0- 37,9 | |||||||||||||
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1.7 −
, . | , . | , . | , % |
8,0 9,9 | 0,5 | ||
10,0 11,9 | 5,0 | ||
12,0 13,9 | 10,0 | ||
14,0 15,9 | 13,0 | ||
16,0 17,9 | 20,0 |
1.7
18,0 19,9 | 29,5 | ||
20,0 21,9 | 43,5 | ||
22,0 23,9 | 61,5 | ||
24,0 25,9 | 74,0 | ||
26,0 27,9 | 81,5 | ||
28,0 29,9 | 88,5 | ||
30,0 31,9 | 95,0 | ||
32,0 33,9 | 97,5 | ||
34,0 35,9 | 98,0 | ||
36,0 37,9 |
1.8 −
, . | , . | , . | , % |
7,0 8,9 | 0,5 | ||
9,0 10,9 | 1,0 | ||
11,0 12,9 | 3,0 | ||
13,0 14,9 | 6,0 | ||
15,0 16,9 | 11,0 | ||
17,0 18,9 | 22,0 | ||
19,0 20,9 | 38,0 | ||
21,0 22,9 | 60,5 | ||
23,0 24,9 | 85,0 | ||
25,0 26,9 | 98,0 | ||
27,0 28,9 | 99,5 | ||
29,0 30,9 |
, %
, .
1.1 −
, %
, .
1.2 −
1.3 −
1.4 −
2.1 −
xj, . | nj, . | xjnj | xj- M | (xj- M)2 | (xj- M)2nj |
9,0 | -13,7 | 187,69 | 187,69 | ||
11,0 | -11,7 | 136,89 | 1232,01 | ||
13,0 | -9,7 | 94,09 | 940,90 | ||
15,0 | -7,7 | 59,29 | 355,74 | ||
17,0 | -5,7 | 32,49 | 454,86 | ||
19,0 | -3,7 | 13,69 | 260,11 | ||
21,0 | -1,7 | 2,89 | 80,92 | ||
23,0 | 0,3 | 0,09 | 3,24 | ||
25,0 | 2,3 | 5,29 | 132,25 | ||
27,0 | 4,3 | 18,49 | 277,35 | ||
29,0 | 6,3 | 39,69 | 555,66 | ||
31,0 | 8,3 | 68,89 | 895,57 | ||
33,0 | 10,3 | 106,09 | 530,45 | ||
35,0 | 12,3 | 151,29 | 151,29 | ||
37,0 | 14,3 | 204,49 | 817,96 | ||
− | − | 6876,00 |
|
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2.1
= ∑xjnj / ∑n (2.1)
= 4530 / 200 = 22,65 ≈ 22,7 .
2.2
σ = √ ∑(xj − M)2 nj / ∑n (2.2)
σ = √ 6876/ 200 = √ 34,38 ≈ 5,86 .
2.3
mM = σ / √ ∑n (2.3)
mM = 5,86/ √200 ≈ 0,41 .
M mM = 22,7 0,41.
2.4
C = σ 100 / M (2.4)
C = 5,86 ∙ 100 / 22,7 = 25,8 %
.
2.5
p = mM ∙ 100 / M (2.5)
p = 0,41 ∙ 100 / 22,7 = 1,8 % ≈ 2 %
2.6
t1 = M / mM (2.6)
t1 = 22,7 / 0,41 = 55
.
2.7
n = ²x² / p² (2.7)
0,68 x = 1,0.
n = 665,64 ∙ 1 / 3,24 = 205
2.8
Me = xmin + i (0,5N − ∑n) / ne (2.8)
22,0 − 23,9 .
x min = 22,0 .;
i = 2 .;
, , ∑nj= 87;
, , ne= 36.
Me = 22,0 + 2 ∙ (0,5 ∙ 200 − 87) / 36 ≈ 22,7 .
, .
, .
2.1 −
22,5 .
Mo = 3Me − 2M (2.9)
Mo = 3 ∙ 22,7 − 2 ∙ 22,7 = 22,7 .
2.2
yj, . | nj, . | yjnj | yj- M | (yj- M)2 | (yj- M)2nj |
8,0 | -13,5 | 182,25 | 182,25 | ||
10,0 | -11,5 | 132,25 | 132,25 | ||
12,0 | -9,5 | 90,25 | 361,00 | ||
14,0 | -7,5 | 56,25 | 337,50 | ||
16,0 | -5,5 | 30,25 | 302,50 | ||
18,0 | -3,5 | 12,25 | 269,50 | ||
20,0 | -1,5 | 2,25 | 72,00 | ||
22,0 | 0,5 | 0,25 | 11,25 | ||
24,0 | 2,5 | 6,25 | 306,25 | ||
26,0 | 4,5 | 20,25 | 526,50 | ||
28,0 | 6,5 | 42,25 | 126,75 | ||
30,0 | 8,5 | 72,25 | 72,25 | ||
− | − |
= 4302 / 200 = 21,51 ≈ 21,5 .
σ = √ 2700 / 200 = √ 13,5 ≈ 3,67 .
mM = 3,67 / √200 ≈ 0,26 .
M mM = 21,5 0,26 .
C = 3,67 ∙ 100 / 21,5 = 17,1 %
.
p = 0,26 ∙ 100 / 21,5 = 1,2 %
t1 = 21,5 / 0,26 = 83
.
0,68 x = 1,0.
n = 17,12 / 1,22 = 292,41 / 1,44 = 203
21,0 − 22,9 .
ymin = 21,0 .;
i = 2 .;
∑nj = 76;
ne = 45.
Me = 21,0 + 2 ∙ (0,5 ∙ 200 − 76) / 45 ≈ 22,1 .
, .
, .
2.2 −
21,9 .
Mo = 3 ∙ 22,1 − 2 ∙ 21,5 = 23,3 .
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