13 Apr 2012 @ 1:40 PM 

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:

Starting digit Occurrences Percent
1 17 27
2 13 21
3 3 4
4 6 9
5 5 8
6 4 6
7 6 9
8 4 6
9 3 4

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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Posted By: Eusebiu Blindu
Last Edit: 13 Apr 2012 @ 08:57 PM

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