prelucrarea statica a datelor
TRANSCRIPT
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Nr.crt Val cresc F m3 m4 f(v)
1 0.86 0.006972 -106.5099 504.8783 0.037188
2 0.87 0.016932 -105.8372 500.6313 0.037644
3 1.45 0.026892 -71.48371 296.6717 0.063614
4 1.48 0.036853 -69.94471 288.1862 0.064914
5 1.55 0.046813 -66.43997 269.0952 0.067923
6 1.91 0.056773 -50.25158 185.4384 0.0827847 1.93 0.066733 -49.43894 181.4508 0.083575
8 2.1 0.076693 -42.88235 150.0968 0.090131
9 2.11 0.086653 -42.51586 148.3888 0.090507
10 2.15 0.096614 -41.07077 141.7024 0.092
11 2.38 0.106574 -33.39247 107.5304 0.100216
12 2.48 0.116534 -30.37717 94.78284 0.103583
13 2.54 0.126494 -28.65823 87.69993 0.10554
14 2.63 0.136454 -26.20337 77.82924 0.108384
15 2.76 0.146414 -22.91114 65.07223 0.112293
16 2.82 0.156375 -21.48959 59.74536 0.11401617 2.88 0.166335 -20.12809 54.75242 0.115686
18 2.96 0.176295 -18.40393 48.59005 0.117831
19 3.04 0.186255 -16.78115 42.9631 0.119879
20 3.37 0.196215 -11.09255 24.73861 0.127281
21 3.4 0.206175 -10.6509 23.43412 0.127869
22 3.49 0.216135 -9.396603 19.82871 0.129546
23 3.51 0.226096 -9.13195 19.0876 0.129901
24 3.62 0.236056 -7.764744 15.37575 0.131739
25 3.62 0.246016 -7.764744 15.37575 0.131739
26 3.66 0.255976 -7.303642 14.17053 0.132359
27 3.7 0.265936 -6.861166 13.03759 0.132953
28 3.71 0.275896 -6.753412 12.7653 0.133097
29 3.81 0.285857 -5.737262 10.27085 0.134453
30 3.82 0.295817 -5.641653 10.04327 0.13458
31 3.93 0.305777 -4.659137 7.78169 0.135867
32 3.98 0.315737 -4.253103 6.890877 0.136388
33 4.01 0.325697 -4.021196 6.394506 0.136681
34 4.16 0.335657 -2.987228 4.302206 0.137931
35 4.19 0.345618 -2.804414 3.954785 0.138138
36 4.23 0.355578 -2.572479 3.524811 0.138392
37 4.28 0.365538 -2.301014 3.037798 0.138675
38 4.29 0.375498 -2.249121 2.946798 0.138726
39 4.3 0.385458 -2.198014 2.857858 0.138777
40 4.43 0.395418 -1.602434 1.875169 0.139288
41 4.55 0.405378 -1.158287 1.216433 0.13953
42 4.65 0.415339 -0.857917 0.815192 0.139567
43 4.68 0.425299 -0.779196 0.717016 0.139549
44 4.84 0.435259 -0.439323 0.333973 0.139234
10
5
10
15
20
25
30
35
Histog
nK
0.1
0.12
0.14
0.16
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45 4.87 0.445219 -0.389337 0.284294 0.139134
46 4.88 0.455179 -0.373559 0.269037 0.139098
47 4.9 0.465139 -0.343294 0.240375 0.139022
48 4.97 0.4751 -0.250285 0.15773 0.138711
49 4.98 0.48506 -0.238559 0.147954 0.138662
50 5.09 0.49502 -0.132807 0.067758 0.138024
51 5.13 0.50498 -0.103956 0.04888 0.13775352 5.17 0.51494 -0.079618 0.034252 0.137461
53 5.29 0.5249 -0.029849 0.009259 0.136462
54 5.51 0.534861 -0.000734 6.62E-005 0.134176
55 5.64 0.544821 6.30E-005 2.51E-006 0.132565
56 5.91 0.554781 0.029733 0.009211 0.128654
57 5.91 0.564741 0.029733 0.009211 0.128654
58 5.97 0.574701 0.050571 0.018701 0.12769
59 6.12 0.584661 0.140446 0.073004 0.125139
60 6.14 0.594622 0.157289 0.084905 0.124784
61 6.16 0.604582 0.175428 0.098205 0.12442662 6.17 0.614542 0.184998 0.105412 0.124246
63 6.18 0.624502 0.19491 0.113009 0.124065
64 6.33 0.634462 0.388697 0.283671 0.12126
65 6.33 0.644422 0.388697 0.283671 0.12126
66 6.33 0.654382 0.388697 0.283671 0.12126
67 6.5 0.664343 0.728514 0.655517 0.117889
68 6.66 0.674303 1.190342 1.261524 0.114552
69 6.74 0.684263 1.480764 1.687775 0.11283
70 6.79 0.694223 1.684309 2.003991 0.111738
71 6.86 0.704183 1.999424 2.518874 0.110189
72 6.87 0.714143 2.047415 2.599808 0.109966
73 6.87 0.724104 2.047415 2.599808 0.109966
74 6.94 0.734064 2.405027 3.222255 0.108393
75 6.95 0.744024 2.459282 3.319538 0.108167
76 6.96 0.753984 2.514346 3.419008 0.10794
77 7.32 0.763944 5.086673 8.748061 0.099563
78 7.53 0.773904 7.186822 13.86913 0.094538
79 7.57 0.783865 7.643045 15.05527 0.093574
80 7.76 0.793825 10.0749 21.75976 0.088979
81 7.89 0.803785 12.00584 27.49098 0.08583
82 7.92 0.813745 12.48394 28.96024 0.085104
83 8.03 0.823705 14.34536 34.85637 0.082446
84 8.05 0.833665 14.70252 36.01824 0.081964
85 8.22 0.843625 17.98061 47.1056 0.077883
86 8.46 0.853586 23.38875 66.88714 0.072203
87 8.49 0.863546 24.13256 69.73827 0.071501
88 8.67 0.873506 28.92879 88.80559 0.067339
89 8.76 0.883466 31.54851 99.68697 0.065292
0
0.02
0.04
0.06
0.08V
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90 8.85 0.893426 34.32179 111.5389 0.06327
91 8.95 0.903386 37.58864 125.9144 0.061055
92 9.55 0.913347 61.62051 243.3887 0.048565
93 10.36 0.923307 107.8366 513.2806 0.034248
94 10.62 0.933267 126.4909 634.959 0.030321
95 10.85 0.943227 144.6866 759.5757 0.027119
96 10.97 0.953187 154.8369 831.4429 0.02554797 11.27 0.963147 182.265 1033.406 0.021912
98 11.57 0.973108 212.7548 1270.104 0.018678
99 12 0.983068 262.1194 1677.512 0.014701
100 17.11 0.993028 1524.766 17549.76 0.000333
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k= 8
plaja= 16.25
h= 2.03 frecventa r
h`= 2.05 16.4
plaja noua= 33.31 est s!"est
v v
# a# $# c# n# f# F#
1 0.86 2.91 1.885 17 0.17 0.17
2 2.91 4.96 3.935 30 0.3 0.47
3 4.96 7.01 5.985 29 0.29 0.76
4 7.01 9.06 8.035 15 0.15 0.91
5 9.06 11.11 10.085 5 0.05 0.96
6 11.11 13.16 12.135 3 0.03 0.99
7 13.16 15.21 14.185 0 0 0.99
8 15.21 17.26 16.235 1 0.01 1
3 4 5 6 7 8
ama frecventelor absolute
R
0 2
0
0.05
0.1
0.150.2
0.25
0.3
0.35
fK
f(v)
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me"a me"a%3 frecventa me"a&frecventa
2.052941176 8.652259 0.17 1.470884
4.029333333 65.41835 0.3 19.62551
6.119655172 229.1822 0.29 66.46283
8.164666667 544.2712 0.15 81.64068
10.47 1147.731 0.05 57.3865411.61333333 1566.285 0.03 46.98854
0 0 0 0
17.11 5008.988 0.01 50.08988
s!ma 323.6649 194.1989
0 2 4 6 8 10 12 14 16
f(v)
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10.6 'e"a
elatva 'e"ana
'"a
$atere me"e a$sl!ta
Varanta
$atere stan"ar"*e+cent "e varate
$# F# *!artle
0.86 0 moment centrat de ordinul 3
2.91 0.17 moment centrat de ordinul
4.96 0.47 *e+cent "e asmetre
7.01 0.76 *e+cent "e $ltre
9.06 0.91 ,tental!l elan
11.11 0.96 a
13.16 0.99 #
15.21 0.99 c17.26 1
ener/a !ntara teretca an!ala
4 6 8 10 12 14 16 18
Frecventa relativa
cK
0
00
0
1
F#
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5.6002
5.11
6.33
2.21
7.86
2.820.50
3.62 5.11 6.95
20.918
288.661
0.96
1.82
194.19892
1.2532845
2.0865
6.3227199.6
180.32535
0 2 4 6 8 10 12 14 16
0
.2
.4
.6
.8
1
.2
Frecvente !umulate
$#
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18 20
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43 -0.591 1.543 2.382 -0.912
44 -0.560 1.577 2.487 -0.883
45 -0.529 1.583 2.506 -0.837
46 -0.499 1.585 2.513 -0.791
47 -0.469 1.589 2.526 -0.745
48 -0.439 1.603 2.571 -0.704
49 -0.410 1.605 2.577 -0.65850 -0.381 1.627 2.648 -0.620
51 -0.352 1.635 2.674 -0.576
52 -0.324 1.643 2.699 -0.532
53 -0.295 1.666 2.775 -0.492
54 -0.267 1.707 2.912 -0.456
55 -0.239 1.730 2.992 -0.414
56 -0.212 1.777 3.156 -0.376
57 -0.184 1.777 3.156 -0.327
58 -0.157 1.787 3.192 -0.280
59 -0.129 1.812 3.282 -0.23460 -0.102 1.815 3.294 -0.185
61 -0.075 1.818 3.305 -0.136
62 -0.048 1.820 3.311 -0.087
63 -0.021 1.821 3.317 -0.038
64 0.006 1.845 3.405 0.012
65 0.033 1.845 3.405 0.062
66 0.061 1.845 3.405 0.112
67 0.088 1.872 3.504 0.164
68 0.115 1.896 3.595 0.218
69 0.142 1.908 3.641 0.271
70 0.170 1.915 3.669 0.325
71 0.197 1.926 3.708 0.380
72 0.225 1.927 3.714 0.434
73 0.253 1.927 3.714 0.487
74 0.281 1.937 3.753 0.544
75 0.309 1.939 3.759 0.600
76 0.338 1.940 3.764 0.656
77 0.367 1.991 3.963 0.731
78 0.397 2.019 4.076 0.801
79 0.426 2.024 4.097 0.863
80 0.457 2.049 4.198 0.936
81 0.488 2.066 4.267 1.007
82 0.519 2.069 4.282 1.074
83 0.551 2.083 4.340 1.149
84 0.584 2.086 4.350 1.219
85 0.618 2.107 4.438 1.302
86 0.653 2.135 4.560 1.394
87 0.689 2.139 4.575 1.474
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88 0.726 2.160 4.665 1.569
89 0.765 2.170 4.710 1.661
90 0.806 2.180 4.754 1.757
91 0.849 2.192 4.803 1.860
92 0.894 2.257 5.092 2.018
93 0.943 2.338 5.466 2.205
94 0.996 2.363 5.583 2.35395 1.054 2.384 5.684 2.513
96 1.119 2.395 5.737 2.680
97 1.194 2.422 5.867 2.892
98 1.285 2.448 5.995 3.147
99 1.406 2.485 6.175 3.493
100 1.603 2.840 8.064 4.551
-56.790 158.556 282.374 -21.435
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100
158.5564
282.3736
-56.78987
-21.43519
-4.080176
2.21516
a 2.21516
$ 6.308721
!0
!1
!2
V0
V1*0
*1
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*lasa
1 17 0.015448 0.179692 16.42436 0.331357 0.0201747392
2 30 0.179692 0.452621 27.29295 7.328102 0.2684979518
3 29 0.452621 0.710687 25.80655 10.19814 0.3951763686
4 15 0.710687 0.879751 16.90642 3.634441 0.2149739753
5 5 0.879751 0.96091 8.115949 9.709135 1.1963032126 3 0.96091 0.990105 2.919513 0.006478 0.0022189259
7 0 0.990105 0.998057 0.795155 0.632272 0.795155105
8 1 0.998057 0.999705 0.164795 0.697567 4.2329297202
7.1254299981
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