Tuesday 17 November 2020

Benford's Law on My Stats


60 numbers start with one
10 thousand and 538, 1482, 13 thousand and 340, 18 thousand and 396, 108 thousand and 940, 1096, 19 thousand and 408, 1707, 155 thousand and 679, 1, 1, 1, 10, 1, 1, 1, 12, 13, 1, 1, 1, 1, 1, 1, 10, 11, 14, 15, 146, 1, 16, 137, 149, 12, 13, 1017, 16, 11, 12, 130, 126, 108, 195, 15, 16, 1368, 141, 19, 18, 1164, 18, 13, 11, 1077, 15, 18, 1633, 143, 1631.

36 numbers start with two
234 thousand and 356 2555 23 thousand and 380 29 thousand and 842 266 thousand and 778 21 thousand and 955 23 thousand and 892 249 thousand and 678 2 2 2 2 2 2 2 2 25 21 28 2 22 24 27 254 22 272 254 2203 20 2621 254 25 232 268 248 28

20 numbers start with three
39 thousand and 657 3966 37 thousand and 548 3447 367 549 343 256 3 3 3 3 3 31 30 3 327 33 349 3589 30 3383

19 numbers start with four
4505 4260 4140 49 thousand and 273 44 thousand and 936 4282 4 4 4 4 4 474 41 43 44 40 483 45 4146

20 numbers start with five
5860 5987 58 thousand and 559 54 thousand and 999 5278 54 5 5 50 5 5 52 5 55 561 5 56 534 55 523

10 numbers start with six
624 65 thousand and 968 6000 6 6 661 64 613 62 669

7 numbers start with seven
7641 75 thousand and 461 785 76 7 70 752

5 numbers start with eight
8 82 8 8 82

5 numbers start with 9
90 thousand and 193 9883 98 98 97

There were also 23 zero values:
0 0 0 0 0 - 0 0 0 0 0 - 0 0 0 0 0 - 0 0 0 0 0 - 0 0 0


60/182 = 0.32967 (start with one)
36/182 = 0.1978 (start with two)
20/182 = 0.10989 (start with three, five)
19/182 = 0.1044 (start with four)
10/182 = 0.05495 (start with six)
7/182 = 0.03846 (start with seven)
5/182 = 0.02747 (start with eight, nine)

Benford's Law - How mathematics can detect fraud!
singingbanana | 9.IV.2011
https://www.youtube.com/watch?v=vIsDjbhbADY


And here is where I took these stats of my viewers from:

New blog on the kid : Repenser les statistiques?
https://nov9blogg9.blogspot.com/2020/10/repenser-les-statistiques.html


It so happens, recently there was a comment on Benford's law in relation to voter fraud. Why do Biden's votes not follow Benford's Law?, by Stand-up Maths. I think there are probably better arguments for Biden supporters faking votes for him and suppressing votes for Trump than lack of conformity with Benford's law in Chicago voting circumscriptions. Anyway, Matt Parker mentioned end digits being even distribution. Here are mine for same statistics:

fourty end in zero
seventeen non-zero end in zero
5860, 4260, 4140, 13 340, 23 380, 108 940, 6000, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 30, 50, 0, 10, 130, 20, 40, 70, 30,
twentysix end in one
7641, 75 461, 1, 1, 1, 1, 1, 1, 11, 21, 31, 1, 1, 1, 1, 1, 1, 1, 11, 141, 41, 661, 561, 2621, 11, 1631,
twentyfour end in two
1482, 29 842, 4282, 23 892, 2, 2, 2, 2, 12, 2, 2, 2 + 2, 82, 52, 12, 2, 22, 12, 22, 272, 82, 62, 752, 232,
twentyone end in three
49 273, 90 193, 9883, 3, 3, 13, 3, 3, 3, 3, 13, 2203, 43, 13, 33, 483, 613, 523, 1633, 143, 3383,
seventeen end in four
624, 4, 4, 54, 4, 14, 4, 4, 24, 474, 254, 254, 1164, 44, 64, 534, 254,
nineteen end in five
4505, 2555, 21 955, 25, 5, 15, 5, 5, 5, 785, 5, 195, 15, 55, 5, 25, 15, 45, 55,
sixteen end in six
234 356, 18 396, 3966, 1096, 44 936, 343 256, 6, 146, 16, 6, 16, 126, 16, 76, 56, 4146,
eleven end in seven
5987, 39 657, 1707, 3447, 137, 17, 27, 327, 7, 1077, 97,
twentyone end in eight
10 538, 65 968, 266 778, 19 408, 37 548, 249 678, 5278, 8, 28, 8, 8, 108, 98, 1368, 18, 18, 268, 248, 28, 98, 18,
nine end in nine
58 559, 54 999, 155 679, 367 549, 149, 19, 349, 3589, 669


As you note, 40 ending in zero is untypical, but 17 non-zero ending in zero is more typical./HGL

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