I am trying to find some use of the Benford’s law in testing.

“Benford’s law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale. Benford’s law also gives the expected distribution for digits beyond the first, which approach a uniform distribution as the digit place goes to the right.” –wikipedia

I thought I found a solution when googling by “1”,”2”,”3” or “one”, “two”, “three” or using even quotes for the same searches to be the exact match. But then I realized that I can hit a search result containing “two hundred and twenty one” when searching for “one” so I am very far from applying the principle in a relevant way.

Well it seems to make some sense though based on the graph, so maybe it’s some sort of applicable variation.

But let’s try something more relevant:

List of countries by number of mobile phones in use

http://en.wikipedia.org/wiki/List_of_countries_by_number_of_mobile_phones_in_use

1	China	1,010,000,000
2	India	911,168,193
3	United States	327,577,529
4	Indonesia	250,100,000
5	Brazil	245,200,000
6	Russia	224,260,000
7	Japan	121,246,700
8	Pakistan	114,610,000
9	Germany	107,000,000
10	Nigeria	90,583,306
11	Mexico	88,797,186
12	Italy	88,580,000
13	Bangladesh	86,550,000
14	Philippines	86,000,000
15	United Kingdom	75,750,000
16	Vietnam	72,300,000
17	Egypt	71,460,000
18	Turkey	66,000,000
19	France	58,730,000
20	Thailand	69,000,000
21	Iran	68,000,000
22	Ukraine	54,377,000
23	South Korea	52,510,000
23	Spain	50,890,000
25	Argentina	50,409,800
26	Poland	47,153,200
27	Colombia	46,147,937
28	South Africa	42,300,000
29	Algeria	33,000,000
30	Venezuela	27,400,000
31	Peru	27,100,000
32	Taiwan	25,412,000
33	Romania	22,800,000
34	Canada	25,543,862
35	Morocco	27,050,000
36	Netherlands	20,000,000
37	Australia	21,260,000
38	Saudi Arabia	46,000,000
39	Malaysia	30,379,000
40	Chile	21,000,000
41	Guatemala	17,571,895
42	Sri Lanka	17,359,312
43	Ecuador	15,900,000
44	Portugal	14,500,000
45	Nepal	14,240,670
46	Hong Kong	13,264,896
47	Belgium	11,822,000
48	Hungary	11,833,000
49	United Arab Emirates	11,540,040
50	Bulgaria	10,655,000
51	Israel	9,319,000
52	Denmark	7,000,000
53	Azerbaijan	7,000,000
54	Jordan	6,010,000
55	Singapore	7,289,000
56	New Zealand	4,620,000
57	Estonia	1,982,000
58	Lebanon	2,720,000
59	Lithuania	4,960,000
60	Montenegro	1,294,167
61	North Korea	1,000,000

Starting digits for the number of mobile phones in this list:

Considering that the data sample has only 61 records and for the first digits we have a success, I think its “relevant enough” and the example is “acceptable”.

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