xi
yi
xi - xśr
(xi-xśr)^2
(xi-xśr)^3
(xi-xśr)^4
yi - yśr
77
59
-46,786
2188,930
-102411,269
4791413,652
-21,038
87
66
-36,786
1353,210
-49779,176
1831176,752
-14,038
87
66
-36,786
1353,210
-49779,176
1831176,752
-14,038
88
66
-35,786
1280,638
-45828,904
1640033,165
-14,038
88
67
-35,786
1280,638
-45828,904
1640033,165
-13,038
89
67
-34,786
1210,066
-42093,349
1464259,231
-13,038
90
67
-33,786
1141,494
-38566,509
1303008,086
-13,038
90
67
-33,786
1141,494
-38566,509
1303008,086
-13,038
91
68
-32,786
1074,922
-35242,386
1155456,868
-12,038
91
68
-32,786
1074,922
-35242,386
1155456,868
-12,038
92
68
-31,786
1010,350
-32114,979
1020806,710
-12,038
92
68
-31,786
1010,350
-32114,979
1020806,710
-12,038
92
68
-31,786
1010,350
-32114,979
1020806,710
-12,038
93
69
-30,786
947,778
-29178,287
898282,751
-11,038
93
69
-30,786
947,778
-29178,287
898282,751
-11,038
93
69
-30,786
947,778
-29178,287
898282,751
-11,038
94
69
-29,786
887,206
-26426,312
787134,124
-11,038
94
69
-29,786
887,206
-26426,312
787134,124
-11,038
95
69
-28,786
828,634
-23853,052
686633,968
-11,038
95
69
-28,786
828,634
-23853,052
686633,968
-11,038
96
69
-27,786
772,062
-21452,509
596079,417
-11,038
96
69
-27,786
772,062
-21452,509
596079,417
-11,038
97
69
-26,786
717,490
-19218,682
514791,607
-11,038
97
69
-26,786
717,490
-19218,682
514791,607
-11,038
98
70
-25,786
664,918
-17145,570
442115,675
-10,038
98
70
-25,786
664,918
-17145,570
442115,675
-10,038
98
70
-25,786
664,918
-17145,570
442115,675
-10,038
98
70
-25,786
664,918
-17145,570
442115,675
-10,038
99
70
-24,786
614,346
-15227,175
377420,757
-10,038
99
70
-24,786
614,346
-15227,175
377420,757
-10,038
99
70
-24,786
614,346
-15227,175
377420,757
-10,038
100
70
-23,786
565,774
-13457,496
320099,988
-10,038
100
70
-23,786
565,774
-13457,496
320099,988
-10,038
100
71
-23,786
565,774
-13457,496
320099,988
-9,038
100
71
-23,786
565,774
-13457,496
320099,988
-9,038
101
71
-22,786
519,202
-11830,532
269570,505
-9,038
101
71
-22,786
519,202
-11830,532
269570,505
-9,038
101
71
-22,786
519,202
-11830,532
269570,505
-9,038
101
71
-22,786
519,202
-11830,532
269570,505
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
71
-21,786
474,630
-10340,285
225273,443
-9,038
102
72
-21,786
474,630
-10340,285
225273,443
-8,038
102
72
-21,786
474,630
-10340,285
225273,443
-8,038
103
72
-20,786
432,058
-8980,753
186673,939
-8,038
103
72
-20,786
432,058
-8980,753
186673,939
-8,038
103
72
-20,786
432,058
-8980,753
186673,939
-8,038
103
72
-20,786
432,058
-8980,753
186673,939
-8,038
103
72
-20,786
432,058
-8980,753
186673,939
-8,038
104
72
-19,786
391,486
-7745,938
153261,128
-8,038
104
72
-19,786
391,486
-7745,938
153261,128
-8,038
104
72
-19,786
391,486
-7745,938
153261,128
-8,038
104
72
-19,786
391,486
-7745,938
153261,128
-8,038
105
72
-18,786
352,914
-6629,839
124548,147
-8,038
105
72
-18,786
352,914
-6629,839
124548,147
-8,038
105
72
-18,786
352,914
-6629,839
124548,147
-8,038
106
72
-17,786
316,342
-5626,455
100072,132
-8,038
106
72
-17,786
316,342
-5626,455
100072,132
-8,038
106
72
-17,786
316,342
-5626,455
100072,132
-8,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
106
73
-17,786
316,342
-5626,455
100072,132
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
73
-16,786
281,770
-4729,788
79394,218
-7,038
107
74
-16,786
281,770
-4729,788
79394,218
-6,038
108
74
-15,786
249,198
-3933,836
62099,542
-6,038
108
74
-15,786
249,198
-3933,836
62099,542
-6,038
108
74
-15,786
249,198
-3933,836
62099,542
-6,038
108
74
-15,786
249,198
-3933,836
62099,542
-6,038
108
74
-15,786
249,198
-3933,836
62099,542
-6,038
109
74
-14,786
218,626
-3232,601
47797,239
-6,038
109
74
-14,786
218,626
-3232,601
47797,239
-6,038
109
74
-14,786
218,626
-3232,601
47797,239
-6,038
109
74
-14,786
218,626
-3232,601
47797,239
-6,038
109
74
-14,786
218,626
-3232,601
47797,239
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
110
74
-13,786
190,054
-2620,082
36120,445
-6,038
111
74
-12,786
163,482
-2090,278
26726,298
-6,038
111
74
-12,786
163,482
-2090,278
26726,298
-6,038
111
74
-12,786
163,482
-2090,278
26726,298
-6,038
111
75
-12,786
163,482
-2090,278
26726,298
-5,038
111
75
-12,786
163,482
-2090,278
26726,298
-5,038
111
75
-12,786
163,482
-2090,278
26726,298
-5,038
111
75
-12,786
163,482
-2090,278
26726,298
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
75
-11,786
138,910
-1637,191
19295,931
-5,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
112
76
-11,786
138,910
-1637,191
19295,931
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
113
76
-10,786
116,338
-1254,819
13534,483
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
114
76
-9,786
95,766
-937,164
9171,088
-4,038
115
76
-8,786
77,194
-678,225
5958,882
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115
76
-8,786
77,194
-678,225
5958,882
-4,038
115
76
-8,786
77,194
-678,225
5958,882
-4,038
115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
-678,225
5958,882
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115
77
-8,786
77,194
-678,225
5958,882
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115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
-678,225
5958,882
-3,038
115
77
-8,786
77,194
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5958,882
-3,038
115
77
-8,786
77,194
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5958,882
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115
77
-8,786
77,194
-678,225
5958,882
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115
77
-8,786
77,194
-678,225
5958,882
-3,038
116
77
-7,786
60,622
-472,001
3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
-472,001
3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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116
77
-7,786
60,622
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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3675,002
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116
77
-7,786
60,622
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116
77
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60,622
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116
77
-7,786
60,622
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3675,002
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117
77
-6,786
46,050
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2120,584
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117
77
-6,786
46,050
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2120,584
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117
77
-6,786
46,050
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2120,584
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117
77
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46,050
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117
78
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117
78
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117
78
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117
78
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2120,584
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118
78
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33,478
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118
78
-5,786
33,478
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118
78
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78
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78
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78
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78
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78
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119
78
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78
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78
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78
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78
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78
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78
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78
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78
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78
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78
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78
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79
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79
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79
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79
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79
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79
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79
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79
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79
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146
89
22,214
493,462
10961,760
243504,544
8,962
146
89
22,214
493,462
10961,760
243504,544
8,962
147
89
23,214
538,890
12509,788
290402,212
8,962
147
89
23,214
538,890
12509,788
290402,212
8,962
147
89
23,214
538,890
12509,788
290402,212
8,962
147
89
23,214
538,890
12509,788
290402,212
8,962
148
89
24,214
586,318
14197,099
343768,558
8,962
148
89
24,214
586,318
14197,099
343768,558
8,962
148
89
24,214
586,318
14197,099
343768,558
8,962
148
89
24,214
586,318
14197,099
343768,558
8,962
148
89
24,214
586,318
14197,099
343768,558
8,962
148
90
24,214
586,318
14197,099
343768,558
9,962
149
90
25,214
635,746
16029,695
404172,717
9,962
149
90
25,214
635,746
16029,695
404172,717
9,962
149
90
25,214
635,746
16029,695
404172,717
9,962
149
90
25,214
635,746
16029,695
404172,717
9,962
150
90
26,214
687,174
18013,574
472207,826
9,962
150
90
26,214
687,174
18013,574
472207,826
9,962
151
90
27,214
740,602
20154,737
548491,020
9,962
151
90
27,214
740,602
20154,737
548491,020
9,962
151
91
27,214
740,602
20154,737
548491,020
10,962
152
91
28,214
796,030
22459,185
633663,436
10,962
152
91
28,214
796,030
22459,185
633663,436
10,962
155
91
31,214
974,314
30412,231
949287,373
10,962
155
91
31,214
974,314
30412,231
949287,373
10,962
156
91
32,214
1037,742
33429,814
1076908,035
10,962
157
92
33,214
1103,170
36640,682
1216983,599
11,962
157
92
33,214
1103,170
36640,682
1216983,599
11,962
157
92
33,214
1103,170
36640,682
1216983,599
11,962
158
92
34,214
1170,598
40050,833
1370299,200
11,962
159
92
35,214
1240,026
43666,268
1537663,975
11,962
160
93
36,214
1311,454
47492,988
1719911,059
12,962
161
94
37,214
1384,882
51536,991
1917897,589
13,962
162
94
38,214
1460,310
55804,279
2132504,700
13,962
162
94
38,214
1460,310
55804,279
2132504,700
13,962
165
95
41,214
1698,594
70005,845
2885220,884
14,962
167
96
43,214
1867,450
80699,975
3487368,741
15,962
171
101
47,214
2229,162
105247,645
4969162,313
20,962
61893
0,000 122158,102
48821,402
86817816,957
(yi-yśr)^2
(yi-yśr)^3
(yi-yśr)^4
442,597
-9311,365
195892,497
197,065
-2766,405
38834,789
Analiza szeregu szczegółowego prostego
197,065
-2766,405
38834,789
197,065
-2766,405
38834,789
Kolumna xi:
169,989
-2216,322
28896,411
169,989
-2216,322
28896,411
Miary położenia
169,989
-2216,322
28896,411
xśr= 123,786
169,989
-2216,322
28896,411
n= 500
144,913
-1744,468
20999,906
Me= 124
144,913
-1744,468
20999,906
Miary zmienności
144,913
-1744,468
20999,906
R= 94
144,913
-1744,468
20999,906
s= 15,631
144,913
-1744,468
20999,906
s^2= 244,316
121,837
-1344,842
14844,363
Vs= 12,627
%
121,837
-1344,842
14844,363
Miary kształtu
121,837
-1344,842
14844,363
As= 0,026
121,837
-1344,842
14844,363
m3= 97,643
121,837
-1344,842
14844,363
K= 2,909
121,837
-1344,842
14844,363
m4= 173635,634
121,837
-1344,842
14844,363
121,837
-1344,842
14844,363
Wnioski: Średnia wartość to 123,786. Srodek naszewgo zbioru czyli mediana to 124. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 94.
121,837
-1344,842
14844,363
Wartości różnią się średnio od wartości średniej o 15,631. Posiadają niewielką asymetrię prawostronną.
121,837
-1344,842
14844,363
Wartości nie są skoncentrowane wokół średniej, czyli dość dużo się od niej różnią.
121,837
-1344,842
14844,363
100,761
-1011,443
10152,869
100,761
-1011,443
10152,869
Kolumna yi
100,761
-1011,443
10152,869
Suma yi=
40019
100,761
-1011,443
10152,869
100,761
-1011,443
10152,869
Miary położenia
100,761
-1011,443
10152,869
xśr= 80,038
średnia arytmetyczna
100,761
-1011,443
10152,869
n= 500
liczebność
100,761
-1011,443
10152,869
Me= 0
mediana (wartość środkowa)
100,761
-1011,443
10152,869
Miary zmienności
81,685
-738,273
6672,512
R= 42
rozrzut
81,685
-738,273
6672,512
s= 6,108
odchylenie standardowe
81,685
-738,273
6672,512
s^2= 37,309
wariancja
81,685
-738,273
6672,512
Vs= 7,631
%
współczynnik zmienności
81,685
-738,273
6672,512
Miary kształtu
81,685
-738,273
6672,512
As= -0,055
współczynnik asymetrii
81,685
-738,273
6672,512
m3= -12,579
moment centralny 3-ego rzędu
81,685
-738,273
6672,512
K= 2,294
współczynnik koncentracji
81,685
-738,273
6672,512
m4= 3192,591
moment centralny 4-ego rzędu
81,685
-738,273
6672,512
81,685
-738,273
6672,512
81,685
-738,273
6672,512
Wnioski: Średnia wartość kolumny yi to 80,038. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 42.
81,685
-738,273
6672,512
Wartości yi różnią się średnio od wartości średniej o 6,108. Posiadają niewielką asymetrię lewostronną
64,609
-519,331
4174,380
Wartości nie są skoncentrowane wokół średniej, czyli dość dużo się od niej różnią.
64,609
-519,331
4174,380
64,609
-519,331
4174,380
64,609
-519,331
4174,380
64,609
-519,331
4174,380
Zamiana szeregu szczegółowego prostego na przedziałowy.
64,609
-519,331
4174,380
64,609
-519,331
4174,380
Szereg xi
64,609
-519,331
4174,380
64,609
-519,331
4174,380
64,609
-519,331
4174,380
64,609
-519,331
4174,380
n=
500
64,609
-519,331
4174,380
Xmin=
77
64,609
-519,331
4174,380
Xmax=
171
64,609
-519,331
4174,380
R=
94
64,609
-519,331
4174,380
k=
9,96597835
64,609
-519,331
4174,380
k=
10
64,609
-519,331
4174,380
dx=
9,4
49,533
-348,616
2453,562
dx=
9,4
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
49,533
-348,616
2453,562
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
Szereg yi
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
n=
500
36,457
-220,130
1329,145
Xmin=
59
36,457
-220,130
1329,145
Xmax=
101
36,457
-220,130
1329,145
R=
42
36,457
-220,130
1329,145
k=
9,96597835
36,457
-220,130
1329,145
k=
10
36,457
-220,130
1329,145
dx=
4,2
36,457
-220,130
1329,145
dx=
4,2
36,457
-220,130
1329,145
36,457
-220,130
1329,145
0
5
10
15
20
25
30
140,7
150,1
159,5
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
36,457
-220,130
1329,145
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
25,381
-127,872
644,218
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
16,305
-65,841
265,868
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
0
20
40
60
80
100
120
140
160
61,1
65,3
69,5
73,7
77,9
Histogram
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
9,229
-28,039
85,183
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
4,153
-8,465
17,251
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
1,077
-1,118
1,161
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,001
0,000
0,000
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
0,925
0,890
0,856
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
3,849
7,553
14,818
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
8,773
25,987
76,973
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
15,697
62,193
246,410
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
24,621
122,172
606,216
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
35,545
211,922
1263,479
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
48,469
337,444
2349,287
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
63,393
504,739
4018,729
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
80,317
719,805
6450,892
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
99,241
988,643
9848,864
120,165
1317,254
14439,734
120,165
1317,254
14439,734
120,165
1317,254
14439,734
120,165
1317,254
14439,734
120,165
1317,254
14439,734
120,165
1317,254
14439,734
143,089
1711,636
20474,589
143,089
1711,636
20474,589
143,089
1711,636
20474,589
143,089
1711,636
20474,589
143,089
1711,636
20474,589
168,013
2177,790
28228,517
194,937
2721,717
38000,607
194,937
2721,717
38000,607
194,937
2721,717
38000,607
223,861
3349,415
50113,946
254,785
4066,885
64915,622
439,405
9210,817
193077,144
18654,278 -6289,615 1596295,301
Analiza szeregu szczegółowego prostego
średnia arytmetyczna
liczebność
mediana (wartość środkowa)
dwa wzory dla parzystych lub nieparzastych
rozrzut
xmax-xmin
odchylenie standardowe
sqrt(s^2)
wariancja
współczynnik zmienności
umiarkowana zmienność danych
współczynnik asymetrii
niewielka asymetria prawostronna (znak +/-)
moment centralny 3-ego rzędu
współczynnik koncentracji
brak koncentracji danych
większe lub mniejsze 3
moment centralny 4-ego rzędu
Wnioski: Średnia wartość to 123,786. Srodek naszewgo zbioru czyli mediana to 124. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 94.
Wartości różnią się średnio od wartości średniej o 15,631. Posiadają niewielką asymetrię prawostronną.
Wartości nie są skoncentrowane wokół średniej, czyli dość dużo się od niej różnią.
średnia arytmetyczna
mediana (wartość środkowa)
dwa wzory dla parzystych lub nieparzastych, chodzi o ilość elemantów
odchylenie standardowe
sqrt(s^2)
s^2 to wariancja - różnica pomiędzy poszczególnymi daneymi srednia sredniej
współczynnik zmienności
ponizej 10 %- mala zmiennosc, 10-20%srednia zmiennosc, pow 20% duza zmiennosc
współczynnik asymetrii
niewielka asymetria lewostronna (znak +/- rodzaj asymetrii), wartosci powyzej sredniej jest wiecej
moment centralny 3-ego rzędu
współczynnik koncentracji
brak koncentracji danych, bo ponizej 3, wartosci odbiegaja od sredniej
moment centralny 4-ego rzędu
Wnioski: Średnia wartość kolumny yi to 80,038. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 42.
Wartości yi różnią się średnio od wartości średniej o 6,108. Posiadają niewielką asymetrię lewostronną
Wartości nie są skoncentrowane wokół średniej, czyli dość dużo się od niej różnią.
Zamiana szeregu szczegółowego prostego na przedziałowy.
k
x0k
x1k
nk
xk
nkskum
fkskum
1
77,0
86,4
1
81,7
1
0,002
2
86,4
95,8
19
91,1
20
0,04
3
95,8
105,2
40
100,5
60
0,12
4
105,2
114,6
73
109,9
133
0,266
5
114,6
124,0
122
119,3
255
0,51
6
124,0
133,4
117
128,7
372
0,744
7
133,4
142,8
67
138,1
439
0,878
8
142,8
152,2
46
147,5
485
0,97
9
152,2
161,6
10
156,9
495
0,99
10
161,6
171,0
5
166,3
500
1
k
x0k
x1k
nk
xk
nkskum
fkskum
1
59,0
63,2
1
61,1
1
0,002
2
63,2
67,4
7
65,3
8
0,016
3
67,4
71,6
38
69,5
46
0,092
4
71,6
75,8
67
73,7
113
0,226
5
75,8
80,0
143
77,9
256
0,512
6
80,0
84,2
123
82,1
379
0,758
7
84,2
88,4
79
86,3
458
0,916
8
88,4
92,6
35
90,5
493
0,986
9
92,6
96,8
6
94,7
499
0,998
10
96,8
101,0
1
98,9
500
1
0
100
200
300
400
500
600
1
20
60
133
255
372
Dystrybuanta
159,5
168,9
178,3
187,7
197,1
206,5
Histogram
77,9
82,1
86,3
90,5
94,7
98,9
istogram
0
100
200
300
400
500
600
0,002
0,016
0,092
0,226
0,512
0,758
Dystrybuanta
Wnioski: Średnia wartość to 123,786. Srodek naszewgo zbioru czyli mediana to 124. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 94.
xn =
250
80 (xn/2)+1=
251
80 Me=
s^2 to wariancja - różnica pomiędzy poszczególnymi daneymi srednia sredniej
ponizej 10 %- mala zmiennosc, 10-20%srednia zmiennosc, pow 20% duza zmiennosc
niewielka asymetria lewostronna (znak +/- rodzaj asymetrii), wartosci powyzej sredniej jest wiecej
Wnioski: Średnia wartość kolumny yi to 80,038. Rozrzut czyli różnica pomiędzy wartością największą i najmniejszą wynosi 42.
372
439
485
495
500
Dystrybuanta
0,758
0,916
0,986
0,998
1
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