Таблицы математической статистики
.pdfТаблицы математической статистики
Таблица 1. Равномерно распределенные случайные числа
10 |
09 |
73 |
25 |
33 |
76 |
52 |
01 |
35 |
86 |
34 |
67 |
35 |
48 |
76 |
37 |
54 |
20 |
48 |
05 |
64 |
69 |
47 |
42 |
96 |
24 |
80 |
52 |
40 |
37 |
08 |
42 |
26 |
89 |
53 |
19 |
64 |
50 |
93 |
03 |
23 |
20 |
90 |
25 |
60 |
99 |
01 |
90 |
25 |
29 |
09 |
37 |
67 |
07 |
15 |
38 |
31 |
13 |
11 |
65 |
12 |
80 |
79 |
99 |
70 |
80 |
15 |
73 |
61 |
47 |
64 |
03 |
23 |
66 |
53 |
80 |
95 |
90 |
91 |
17 |
39 |
29 |
27 |
49 |
45 |
66 |
06 |
57 |
47 |
17 |
20 |
63 |
61 |
04 |
02 |
00 |
82 |
29 |
16 |
65 |
31 |
06 |
01 |
08 |
05 |
15 |
95 |
33 |
47 |
64 |
35 |
08 |
03 |
36 |
06 |
85 |
26 |
97 |
76 |
02 |
88 |
67 |
67 |
43 |
97 |
04 |
43 |
62 |
76 |
59 |
63 |
57 |
33 |
21 |
35 |
96 |
95 |
11 |
68 |
77 |
12 |
17 |
17 |
68 |
33 |
73 |
79 |
64 |
57 |
53 |
34 |
07 |
27 |
68 |
50 |
36 |
69 |
73 |
61 |
70 |
65 |
81 |
33 |
98 |
85 |
45 |
57 |
18 |
24 |
06 |
35 |
30 |
34 |
26 |
14 |
86 |
79 |
90 |
74 |
39 |
02 |
05 |
16 |
56 |
92 |
68 |
66 |
57 |
48 |
18 |
73 |
05 |
38 |
52 |
47 |
05 |
32 |
54 |
70 |
48 |
90 |
55 |
35 |
75 |
48 |
28 |
46 |
82 |
87 |
09 |
03 |
53 |
96 |
47 |
78 |
35 |
80 |
83 |
42 |
82 |
60 |
93 |
52 |
03 |
44 |
11 |
19 |
92 |
91 |
70 |
98 |
52 |
01 |
77 |
67 |
14 |
90 |
56 |
86 |
07 |
23 |
40 |
30 |
97 |
32 |
11 |
80 |
50 |
54 |
31 |
39 |
80 |
82 |
77 |
32 |
18 |
62 |
38 |
85 |
79 |
83 |
45 |
29 |
96 |
34 |
06 |
28 |
89 |
80 |
83 |
83 |
49 |
12 |
56 |
24 |
86 |
68 |
54 |
02 |
00 |
86 |
50 |
75 |
84 |
01 |
35 |
27 |
38 |
84 |
35 |
99 |
59 |
46 |
73 |
48 |
87 |
51 |
76 |
49 |
69 |
22 |
10 |
94 |
05 |
58 |
60 |
97 |
09 |
34 |
33 |
50 |
50 |
07 |
39 |
98 |
50 |
72 |
56 |
82 |
48 |
29 |
40 |
52 |
42 |
01 |
52 |
77 |
56 |
78 |
61 |
13 |
74 |
67 |
00 |
78 |
18 |
47 |
54 |
06 |
10 |
68 |
71 |
17 |
78 |
17 |
36 |
76 |
66 |
73 |
51 |
90 |
36 |
47 |
64 |
93 |
29 |
60 |
91 |
10 |
62 |
91 |
82 |
60 |
89 |
28 |
93 |
78 |
56 |
13 |
68 |
23 |
47 |
83 |
41 |
13 |
65 |
48 |
11 |
76 |
74 |
17 |
46 |
85 |
09 |
50 |
58 |
04 |
77 |
69 |
74 |
80 |
12 |
43 |
56 |
35 |
17 |
72 |
70 |
80 |
15 |
45 |
31 |
82 |
23 |
74 |
74 |
35 |
09 |
98 |
17 |
77 |
40 |
27 |
72 |
14 |
43 |
23 |
60 |
02 |
10 |
69 |
91 |
62 |
68 |
03 |
66 |
25 |
22 |
91 |
48 |
36 |
93 |
68 |
72 |
03 |
09 |
89 |
32 |
05 |
05 |
14 |
22 |
56 |
85 |
14 |
46 |
42 |
75 |
67 |
88 |
Таблица 2. Значения квантилей распределения Стьюдента
Число степеней |
Доверительные вероятности |
|
|
||
свободы |
0.9 |
0.95 |
0.98 |
0.99 |
0.999 |
1 |
6.31375 |
12.7062 |
31.821 |
63.655898 |
636.578 |
2 |
2.91999 |
4.30266 |
6.96455 |
9.9249883 |
31.5998 |
3 |
2.35336 |
3.18245 |
4.54071 |
5.8408477 |
12.9244 |
4 |
2.13185 |
2.77645 |
3.74694 |
4.6040805 |
8.61008 |
5 |
2.01505 |
2.57058 |
3.36493 |
4.0321174 |
6.8685 |
6 |
1.94318 |
2.44691 |
3.14267 |
3.7074278 |
5.95872 |
7 |
1.89458 |
2.36462 |
2.99795 |
3.499481 |
5.40807 |
8 |
1.85955 |
2.30601 |
2.89647 |
3.3553806 |
5.04137 |
9 |
1.83311 |
2.26216 |
2.82143 |
3.2498428 |
4.78089 |
10 |
1.81246 |
2.22814 |
2.76377 |
3.1692616 |
4.58676 |
11 |
1.79588 |
2.20099 |
2.71808 |
3.1058153 |
4.43688 |
12 |
1.78229 |
2.17881 |
2.68099 |
3.054538 |
4.31784 |
13 |
1.77093 |
2.16037 |
2.6503 |
3.0122828 |
4.22093 |
14 |
1.76131 |
2.14479 |
2.62449 |
2.9768489 |
4.14031 |
15 |
1.75305 |
2.13145 |
2.60248 |
2.9467265 |
4.07279 |
16 |
1.74588 |
2.1199 |
2.58349 |
2.9207877 |
4.01487 |
17 |
1.73961 |
2.10982 |
2.56694 |
2.8982322 |
3.96511 |
18 |
1.73406 |
2.10092 |
2.55238 |
2.8784416 |
3.92174 |
19 |
1.72913 |
2.09302 |
2.53948 |
2.8609429 |
3.88332 |
20 |
1.72472 |
2.08596 |
2.52798 |
2.845336 |
3.84956 |
21 |
1.72074 |
2.07961 |
2.51765 |
2.8313661 |
3.8193 |
22 |
1.71714 |
2.07388 |
2.50832 |
2.8187605 |
3.79223 |
23 |
1.71387 |
2.06865 |
2.49987 |
2.8073373 |
3.76764 |
24 |
1.71088 |
2.0639 |
2.49216 |
2.7969509 |
3.74537 |
25 |
1.70814 |
2.05954 |
2.4851 |
2.7874376 |
3.72514 |
26 |
1.70562 |
2.05553 |
2.47863 |
2.7787246 |
3.70666 |
27 |
1.70329 |
2.05183 |
2.47266 |
2.7706847 |
3.68949 |
28 |
1.70113 |
2.04841 |
2.46714 |
2.7632632 |
3.67392 |
29 |
1.69913 |
2.04523 |
2.46202 |
2.7563874 |
3.65952 |
30 |
1.69726 |
2.04227 |
2.45726 |
2.7499846 |
3.64598 |
60 |
1.67065 |
2.0003 |
2.39012 |
2.660272 |
3.46015 |
120 |
1.65765 |
1.97993 |
2.35783 |
2.6174166 |
3.37342 |
Таблица 3. Значения нормальной стандартной функции распределения
х |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
0 |
0.5 |
0.3 |
0.6179 |
0.6 |
0.7257 |
0.9 |
0.8159 |
0.01 |
0.504 |
0.31 |
0.6217 |
0.61 |
0.7291 |
0.91 |
0.8186 |
0.02 |
0.508 |
0.32 |
0.6255 |
0.62 |
0.7324 |
0.92 |
0.8212 |
0.03 |
0.512 |
0.33 |
0.6293 |
0.63 |
0.7357 |
0.93 |
0.8238 |
0.04 |
0.516 |
0.34 |
0.6331 |
0.64 |
0.7389 |
0.94 |
0.8264 |
0.05 |
0.5199 |
0.35 |
0.6368 |
0.65 |
0.7422 |
0.95 |
0.8289 |
0.06 |
0.5239 |
0.36 |
0.6406 |
0.66 |
0.7454 |
0.96 |
0.8315 |
0.07 |
0.5279 |
0.37 |
0.6443 |
0.67 |
0.7486 |
0.97 |
0.834 |
0.08 |
0.5319 |
0.38 |
0.648 |
0.68 |
0.7517 |
0.98 |
0.8365 |
0.09 |
0.5359 |
0.39 |
0.6517 |
0.69 |
0.7549 |
0.99 |
0.8389 |
0.1 |
0.5398 |
0.4 |
0.6554 |
0.7 |
0.758 |
1 |
0.8413 |
0.11 |
0.5438 |
0.41 |
0.6591 |
0.71 |
0.7611 |
1.01 |
0.8438 |
0.12 |
0.5478 |
0.42 |
0.6628 |
0.72 |
0.7642 |
1.02 |
0.8461 |
0.13 |
0.5517 |
0.43 |
0.6664 |
0.73 |
0.7673 |
1.03 |
0.8485 |
0.14 |
0.5557 |
0.44 |
0.67 |
0.74 |
0.7704 |
1.04 |
0.8508 |
0.15 |
0.5596 |
0.45 |
0.6736 |
0.75 |
0.7734 |
1.05 |
0.8531 |
0.16 |
0.5636 |
0.46 |
0.6772 |
0.76 |
0.7764 |
1.06 |
0.8554 |
0.17 |
0.5675 |
0.47 |
0.6808 |
0.77 |
0.7794 |
1.07 |
0.8577 |
0.18 |
0.5714 |
0.48 |
0.6844 |
0.78 |
0.7823 |
1.08 |
0.8599 |
0.19 |
0.5753 |
0.49 |
0.6879 |
0.79 |
0.7852 |
1.09 |
0.8621 |
0.2 |
0.5793 |
0.5 |
0.6915 |
0.8 |
0.7881 |
1.1 |
0.8643 |
0.21 |
0.5832 |
0.51 |
0.695 |
0.81 |
0.791 |
1.11 |
0.8665 |
0.22 |
0.5871 |
0.52 |
0.6985 |
0.82 |
0.7939 |
1.12 |
0.8686 |
0.23 |
0.591 |
0.53 |
0.7019 |
0.83 |
0.7967 |
1.13 |
0.8708 |
0.24 |
0.5948 |
0.54 |
0.7054 |
0.84 |
0.7995 |
1.14 |
0.8729 |
0.25 |
0.5987 |
0.55 |
0.7088 |
0.85 |
0.8023 |
1.15 |
0.8749 |
0.26 |
0.6026 |
0.56 |
0.7123 |
0.86 |
0.8051 |
1.16 |
0.877 |
0.27 |
0.6064 |
0.57 |
0.7157 |
0.87 |
0.8078 |
1.17 |
0.879 |
0.28 |
0.6103 |
0.58 |
0.719 |
0.88 |
0.8106 |
1.18 |
0.881 |
0.29 |
0.6141 |
0.59 |
0.7224 |
0.89 |
0.8133 |
1.19 |
0.883 |
Продолжение таблицы 3
х |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
1.2 |
0.8849 |
1.5 |
0.9332 |
1.8 |
0.9641 |
2.1 |
0.9821 |
1.21 |
0.8869 |
1.51 |
0.9345 |
1.81 |
0.9649 |
2.11 |
0.9826 |
1.22 |
0.8888 |
1.52 |
0.9357 |
1.82 |
0.9656 |
2.12 |
0.983 |
1.23 |
0.8907 |
1.53 |
0.937 |
1.83 |
0.9664 |
2.13 |
0.9834 |
1.24 |
0.8925 |
1.54 |
0.9382 |
1.84 |
0.9671 |
2.14 |
0.9838 |
1.25 |
0.8944 |
1.55 |
0.9394 |
1.85 |
0.9678 |
2.15 |
.0.9842 |
1.26 |
0.8962 |
1.56 |
0.9406 |
1.86 |
0.9686 |
2.16 |
0.9846 |
1.27 |
0.898 |
1.57 |
0.9418 |
1.87 |
0.9693 |
2.17 |
0.985 |
1.28 |
0.8997 |
1.58 |
0.9429 |
1.88 |
0.9699 |
2.18 |
0.9854 |
1.29 |
0.9015 |
1.59 |
0.9441 |
1.89 |
0.9706 |
2.19 |
0.9857 |
1.3 |
0.9032 |
1.6 |
0.9452 |
1.9 |
0.9713 |
2.2 |
0.9861 |
1.31 |
0.9049 |
1.61 |
0.9463 |
1.91 |
0.9719 |
2.21 |
0.9864 |
1.32 |
0.9066 |
1.62 |
0.9474 |
1.92 |
0.9726 |
2.22 |
0.9868 |
1.33 |
0.9082 |
1.63 |
0.9484 |
1.93 |
0.9732 |
2.23 |
0.9871 |
1.34 |
0.9099 |
1.64 |
0.9495 |
1.94 |
0.9738 |
2.24 |
0.9875 |
1.35 |
0.9115 |
1.65 |
0.9505 |
1.95 |
0.9744 |
2.25 |
0.9878 |
1.36 |
0.9131 |
1.66 |
0.9515 |
1.96 |
0.975 |
2.26 |
0.9881 |
1.37 |
0.9147 |
1.67 |
0.9525 |
1.97 |
0.9756 |
2.27 |
0.9884 |
1.38 |
0.9162 |
1.68 |
0.9535 |
1.98 |
0.9761 |
2.28 |
0.9887 |
1.39 |
0.9177 |
1.69 |
0.9545 |
1.99 |
0.9767 |
2.29 |
0.989 |
1.4 |
0.9192 |
1.7 |
0.9554 |
2 |
0.9772 |
2.3 |
0.9893 |
1.41 |
0.9207 |
1.71 |
0.9564 |
2.01 |
0.9778 |
2.31 |
0.9896 |
1.42 |
0.9222 |
1.72 |
0.9573 |
2.02 |
0.9783 |
2.32 |
0.9898 |
1.43 |
0.9236 |
1.73 |
0.9582 |
2.03 |
0.9788 |
2.33 |
0.9901 |
1.44 |
0.9251 |
1.74 |
0.9591 |
2.04 |
0.9793 |
2.34 |
0.9904 |
1.45 |
0.9265 |
1.75 |
0.9599 |
2.05 |
0.9798 |
2.35 |
0.9906 |
1.46 |
0.9279 |
1.76 |
0.9608 |
2.06 |
0.9803 |
2.36 |
0.9909 |
1.47 |
0.9292 |
1.77 |
0.9616 |
2.07 |
0.9808 |
2.37 |
0.9911 |
1.48 |
0.9306 |
1.78 |
0.9625 |
2.08 |
0.9812 |
2.38 |
0.9913 |
1.49 |
0.9319 |
1.79 |
0.9633 |
2.09 |
0.9817 |
2.39 |
0.9916 |
Окончание таблицы 3
х |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
X |
Ф(х) |
2.4 |
0.9918 |
2.7 |
0.9965 |
3 |
0.9987 |
3.3 |
0.9995 |
2.41 |
0.992 |
2.71 |
0.9966 |
3.01 |
0.9987 |
3.31 |
0.9995 |
2.42 |
0.9922 |
2.72 |
0.9967 |
3.02 |
0.9987 |
3.32 |
0.9995 |
2.43 |
0.9925 |
2.73 |
0.9968 |
3.03 |
0.9988 |
3.33 |
0.9996 |
2.44 |
0.9927 |
2.74 |
0.9969 |
3.04 |
0.9988 |
3.34 |
0.9996 |
2.45 |
0.9929 |
2.75 |
0.997 |
3.05 |
0.9989 |
3.35 |
0.9996 |
2.46 |
0.9931 |
2.76 |
0.9971 |
3.06 |
0.9989 |
3.36 |
0.9996 |
2.47 |
0.9932 |
2.77 |
0.9972 |
3.07 |
0.9989 |
3.37 |
0.9996 |
2.48 |
0.9934 |
2.78 |
0.9973 |
3.08 |
0.999 |
3.38 |
0.9996 |
2.49 |
0.9936 |
2.79 |
0.9974 |
3.09 |
0.999 |
3.39 |
0.9997 |
2.5 |
0.9938 |
2.8 |
0.9974 |
3.1 |
0.999 |
3.4 |
0.9997 |
2.51 |
0.994 |
2.81 |
0.9975 |
3.11 |
0.9991 |
3.41 |
0.9997 |
2.52 |
0.9941 |
2.82 |
0.9976 |
3.12 |
0.9991 |
3.42 |
0.9997 |
2.53 |
0.9943 |
2.83 |
0.9977 |
3.13 |
0.9991 |
3.43 |
0.9997 |
2.54 |
0.9945 |
2.84 |
0.9977 |
3.14 |
0.9992 |
3.44 |
0.9997 |
2.55 |
0.9946 |
2.85 |
0.9978 |
3.15 |
0.9992 |
3.45 |
0.9997 |
2.56 |
0.9948 |
2.86 |
0.9979 |
3.16 |
0.9992 |
3.46 |
0.9997 |
2.57 |
0.9949 |
2.87 |
0.9979 |
3.17 |
0.9992 |
3.47 |
0.9997 |
2.58 |
0.9951 |
2.88 |
0.998 |
3.18 |
0.9993 |
3.48 |
0.9997 |
2.59 |
0.9952 |
2.89 |
0.9981 |
3.19 |
0.9993 |
3.49 |
0.9998 |
2.6 |
0.9953 |
2.9 |
0.9981 |
3.2 |
0.9993 |
3.5 |
0.9998 |
2.61 |
0.9955 |
2.91 |
0.9982 |
3.21 |
0.9993 |
3.6 |
0.9998 |
2.62 |
0.9956 |
2.92 |
0.9982 |
3.22 |
0.9994 |
3.7 |
0.9998 |
2.63 |
0.9957 |
2.93 |
0.9983 |
3.23 |
0.9994 |
3.8 |
0.9999 |
2.64 |
0.9959 |
2.94 |
0.9984 |
3.24 |
0.9994 |
3.9 |
1 |
2.65 |
0.996 |
2.95 |
0.9984 |
3.25 |
0.9994 |
4 |
1 |
' 2.66 |
0.9961 |
2.96 |
0.9985 |
3.26 |
0.9994 |
|
|
2.67 |
0.9962 |
2.97 |
0.9985 |
3.27 |
0.9995 |
|
|
2.68 |
0.9963 |
2.98 |
0.9986 |
3.28 |
0.9995 |
|
|
2.69 |
0.9964 |
2.99 |
0.9986 |
3.29 |
0.9995 |
|
|
Таблица4. Значения квантилей распределения Пирсона
Число степеней |
|
|
Уровень значимости |
|
|
|||
свободы |
|
|
|
|
0.025 |
|
|
|
0.001 |
0.005 |
|
0.01 |
|
0.05 |
0.1 |
||
1 |
10.827 |
7.879 |
|
6.635 |
5.024 |
|
3.841 |
2.706 |
2 |
13.815 |
10.6 |
|
9.21 |
7.378 |
|
5.991 |
4.605 |
3 |
16.266 |
12.84 |
|
11.34 |
9.348 |
|
7.815 |
6.251 |
4 |
18.466 |
14.86 |
|
13.28 |
11.14 |
|
9.488 |
7.779 |
5 |
20.515 |
16.75 |
|
15.09 |
12.83 |
|
11.07 |
9.236 |
6 |
22.457 |
18.55 |
|
16.81 |
14.45 |
|
12.59 |
10.64 |
7 |
24.321 |
20.28 |
|
18.48 |
16.01 |
|
14.07 |
12.02 |
8 |
26.124 |
21.95 |
|
20.09 |
17.53 |
|
15.51 |
13.36 |
9 |
27.877 |
23.59 |
|
21.67 |
19.02 |
|
16.92 |
14.68 |
10 |
29.588 |
25.19 |
|
23.21 |
20.48 |
|
18.31 |
15.99 |
11 |
31.264 |
26.76 |
|
24.73 |
21.92 |
|
19.68 |
17.28 |
12 |
32.909 |
28.3 |
|
26.22 |
23.34 |
|
21.03 |
18.55 |
13 |
34.527 |
29.82 |
|
27.69 |
24.74 |
|
22.36 |
19.81 |
14 |
36.124 |
31.32 |
|
29.14 |
26.12 |
|
23.68 |
21.06 |
15 |
37.698 |
32.8 |
|
30.58 |
27.49 |
|
25 |
22.31 |
16 |
39.252 |
34.27 |
|
32 |
28.85 |
|
26.3 |
23.54 |
17 |
40.791 |
35.72 |
|
33.41 |
30.19 |
|
27.59 |
24.77 |
18 |
42.312 |
37.16 |
|
34.81 |
31.53 |
|
28.87 |
25.99 |
19 |
43.819 |
38.58 |
|
36.19 |
32.85 |
|
30.14 |
27.2 |
20 |
45.314 |
40 |
|
37.57 |
34.17 |
|
31.41 |
28.41 |
21 |
46.796 |
41.4 |
|
38.93 |
35.48 |
|
32.67 |
29.62 |
22 |
48.268 |
42.8 |
|
40.29 |
36.78 |
|
33.92 |
30.81 |
23 |
49.728 |
44.18 |
|
41.64 |
38.08 |
|
35.17 |
32.01 |
24 |
51.179 |
45.56 |
|
42.98 |
39.36 |
|
36.42 |
33.2 |
25 |
52.619 |
46.93 |
|
44.31 |
40.65 |
|
37.65 |
34.38 |
26 |
54.051 |
48.29 |
|
45.64 |
41.92 |
|
38.89 |
35.56 |
27 |
55.475 |
49.65 |
|
46.96 |
43.19 |
|
40.11 |
36.74 |
28 |
56.892 |
50.99 |
|
48.28 |
44.46 |
|
41.34 |
37.92 |
29 |
58.301 |
52.34 |
|
49.59 |
45.72 |
|
42.56 |
39.09 |
30 |
59.702 |
53.67 |
|
50.89 |
46.98 |
|
43.77 |
40.26 |