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File:Benfords law illustrated by world's countries population.png

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Summary[edit]

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Description
English: illustration of Benford's law, using the population of the countries of the world.

The chart depicts the percentage of countries having the corresponding digit as first digit of their population (red bars). For example, 64 countries of 237 (=27%) have 1 as leading digit of the population. Black points indicate what is predicted by Benford's law.

the data is from CIA Worldbook https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html, accessed August 07, 2010

Rank|| country Population Date of Information ||1 China ||1,330,141,295|| ||July 2010 2 India ||1,173,108,018|| ||July 2010 3 United States ||310,232,863|| ||July 2010 4 Indonesia ||242,968,342|| ||July 2010 5 Brazil ||201,103,330|| ||July 2010 6 Pakistan ||177,276,594|| ||July 2010 7 Bangladesh ||158,065,841|| ||July 2010 8 Nigeria ||152,217,341|| ||July 2010 9 Russia ||139,390,205|| ||July 2010 10 Japan ||126,804,433|| ||July 2010 11 Mexico ||112,468,855|| ||July 2010 12 Philippines ||99,900,177|| ||July 2010 13 Vietnam ||89,571,130|| ||July 2010 14 Ethiopia ||88,013,491|| ||July 2010 15 Germany ||82,282,988|| ||July 2010 16 Egypt ||80,471,869|| ||July 2010 17 Turkey ||77,804,122|| ||July 2010 18 Congo, Democratic Republic of the ||70,916,439|| ||July 2010 19 Iran ||67,037,517|| ||July 2010 20 Thailand ||66,404,688|| ||July 2010 21 France ||64,057,792|| ||July 2010 22 United Kingdom ||61,284,806|| ||July 2010 23 Italy ||58,090,681|| ||July 2010 24 Burma ||53,414,374|| ||July 2010 25 South Africa ||49,109,107|| ||July 2010 26 Korea, South ||48,636,068|| ||July 2010 27 Ukraine ||45,415,596|| ||July 2010 28 Colombia ||44,205,293|| ||July 2010 29 Sudan ||41,980,182|| ||July 2010 30 Tanzania ||41,892,895|| ||July 2010 31 Argentina ||41,343,201|| ||July 2010 32 Spain ||40,548,753|| ||July 2010 33 Kenya ||40,046,566|| ||July 2010 34 Poland ||38,463,689|| ||July 2010 35 Algeria ||34,586,184|| ||July 2010 36 Canada ||33,759,742|| ||July 2010 37 Uganda ||33,398,682|| ||July 2010 38 Morocco ||31,627,428|| ||July 2010 39 Peru ||29,907,003|| ||July 2010 40 Iraq ||29,671,605|| ||July 2010 41 Saudi Arabia ||29,207,277|| ||July 2010 42 Afghanistan ||29,121,286|| ||July 2010 43 Nepal ||28,951,852|| ||July 2010 44 Uzbekistan ||27,865,738|| ||July 2010 45 Venezuela ||27,223,228|| ||July 2010 46 Malaysia ||26,160,256|| ||July 2010 47 Ghana ||24,339,838|| ||July 2010 48 Yemen ||23,495,361|| ||July 2010 49 Taiwan ||23,024,956|| ||July 2010 50 Korea, North ||22,757,275|| ||July 2010 51 Syria ||22,198,110|| ||July 2010 52 Romania ||22,181,287|| ||July 2010 53 Mozambique ||22,061,451|| ||July 2010 54 Australia ||21,515,754|| ||July 2010 55 Sri Lanka ||21,513,990|| ||July 2010 56 Madagascar ||21,281,844|| ||July 2010 57 Cote d'Ivoire ||21,058,798|| ||July 2010 58 Cameroon ||19,294,149|| ||July 2010 59 Netherlands ||16,783,092|| ||July 2010 60 Chile ||16,746,491|| ||July 2010 61 Burkina Faso ||16,241,811|| ||July 2010 62 Niger ||15,878,271|| ||July 2010 63 Kazakhstan ||15,460,484|| ||July 2010 64 Malawi ||15,447,500|| ||July 2010 65 Ecuador ||14,790,608|| ||July 2010 66 Cambodia ||14,753,320|| ||July 2010 67 Senegal ||14,086,103|| ||July 2010 68 Mali ||13,796,354|| ||July 2010 69 Guatemala ||13,550,440|| ||July 2010 70 Angola ||13,068,161|| ||July 2010 71 Zambia ||12,056,923|| ||July 2010 72 Zimbabwe ||11,651,858|| ||July 2010 73 Cuba ||11,477,459|| ||July 2010 74 Rwanda ||11,055,976|| ||July 2010 75 Greece ||10,749,943|| ||July 2010 76 Portugal ||10,735,765|| ||July 2010 77 Tunisia ||10,589,025|| ||July 2010 78 Chad ||10,543,464|| ||July 2010 79 Belgium ||10,423,493|| ||July 2010 80 Guinea ||10,324,025|| ||July 2010 81 Czech Republic ||10,201,707|| ||July 2010 82 Somalia ||10,112,453|| ||July 2010 83 Bolivia ||9,947,418|| ||July 2010 84 Hungary ||9,880,059|| ||July 2010 85 Burundi ||9,863,117|| ||July 2010 86 Dominican Republic ||9,794,487|| ||July 2010 87 Belarus ||9,612,632|| ||July 2010 88 Haiti ||9,203,083|| ||July 2010 89 Sweden ||9,074,055|| ||July 2010 90 Benin ||9,056,010|| ||July 2010 91 Azerbaijan ||8,303,512|| ||July 2010 92 Austria ||8,214,160|| ||July 2010 93 Honduras ||7,989,415|| ||July 2010 94 Switzerland ||7,623,438|| ||July 2010 95 Tajikistan ||7,487,489|| ||July 2010 96 Israel ||7,353,985|| ||July 2010 97 Serbia ||7,344,847|| ||July 2010 98 Bulgaria ||7,148,785|| ||July 2010 99 Hong Kong ||7,089,705|| ||July 2010 100 Laos ||6,993,767|| ||July 2010 101 Libya ||6,461,454|| ||July 2010 102 Jordan ||6,407,085|| ||July 2010 103 Paraguay ||6,375,830|| ||July 2010 104 Togo ||6,199,841|| ||July 2010 105 Papua New Guinea ||6,064,515|| ||July 2010 106 El Salvador ||6,052,064|| ||July 2010 107 Nicaragua ||5,995,928|| ||July 2010 108 Eritrea ||5,792,984|| ||July 2010 109 Denmark ||5,515,575|| ||July 2010 110 Kyrgyzstan ||5,508,626|| ||July 2010 111 Slovakia ||5,470,306|| ||July 2010 112 Finland ||5,255,068|| ||July 2010 113 Sierra Leone ||5,245,695|| ||July 2010 114 United Arab Emirates ||4,975,593|| ||July 2010 115 Turkmenistan ||4,940,916|| ||July 2010 116 Central African Republic ||4,844,927|| ||July 2010 117 Singapore ||4,701,069|| ||July 2010 118 Norway ||4,676,305|| ||July 2010 119 Bosnia and Herzegovina ||4,621,598|| ||July 2010 120 Georgia ||4,600,825|| ||July 2010 121 Costa Rica ||4,516,220|| ||July 2010 122 Croatia ||4,486,881|| ||July 2010 123 Moldova ||4,317,483|| ||July 2010 124 New Zealand ||4,252,277|| ||July 2010 125 Ireland ||4,250,163|| ||July 2010 126 Congo, Republic of the ||4,125,916|| ||July 2010 127 Lebanon ||4,125,247|| ||July 2010 128 Puerto Rico ||3,977,663|| ||July 2010 129 Liberia ||3,685,076|| ||July 2010 130 Albania ||3,659,616|| ||July 2010 131 Lithuania ||3,545,319|| ||July 2010 132 Uruguay ||3,510,386|| ||July 2010 133 Panama ||3,410,676|| ||July 2010 134 Mauritania ||3,205,060|| ||July 2010 135 Mongolia ||3,086,918|| ||July 2010 136 Oman ||2,967,717|| ||July 2010 137 Armenia ||2,966,802|| ||July 2010 138 Jamaica ||2,847,232|| ||July 2010 139 Kuwait ||2,789,132|| ||July 2010 140 West Bank ||2,514,845|| ||July 2010 141 Latvia ||2,217,969|| ||July 2010 142 Namibia ||2,128,471|| ||July 2010 143 Macedonia ||2,072,086|| ||July 2010 144 Botswana ||2,029,307|| ||July 2010 145 Slovenia ||2,003,136|| ||July 2010 146 Lesotho ||1,919,552|| ||July 2010 147 Gambia, The ||1,824,158|| ||July 2010 148 Kosovo ||1,815,048|| ||July 2010 149 Gaza Strip ||1,604,238|| ||July 2010 150 Guinea-Bissau ||1,565,126|| ||July 2010 151 Gabon ||1,545,255|| ||July 2010 152 Swaziland ||1,354,051|| ||July 2010 153 Mauritius ||1,294,104|| ||July 2010 154 Estonia ||1,291,170|| ||July 2010 155 Trinidad and Tobago ||1,228,691|| ||July 2010 156 Timor-Leste ||1,154,625|| ||July 2010 157 Cyprus ||1,102,677|| ||July 2010 158 Fiji ||957,780|| ||July 2010 159 Qatar ||840,926|| ||July 2010 160 Comoros ||773,407|| ||July 2010 161 Guyana ||748,486|| ||July 2010 162 Djibouti ||740,528|| ||July 2010 163 Bahrain ||738,004|| ||July 2010 164 Bhutan ||699,847|| ||July 2010 165 Montenegro ||666,730|| ||July 2010 166 Equatorial Guinea ||650,702|| ||July 2010 167 Solomon Islands ||609,794|| ||July 2010 168 Macau ||567,957|| ||July 2010 169 Cape Verde ||508,659|| ||July 2010 170 Luxembourg ||497,538|| ||July 2010 171 Western Sahara ||491,519|| ||July 2010 172 Suriname ||486,618|| ||July 2010 173 Malta ||406,771|| ||July 2010 174 Maldives ||395,650|| ||July 2010 175 Brunei ||395,027|| ||July 2010 176 Belize ||314,522|| ||July 2010 177 Bahamas, The ||310,426|| ||July 2010 178 Iceland ||308,910|| ||July 2010 179 French Polynesia ||291,000|| ||July 2010 180 Barbados ||285,653|| ||July 2010 181 Mayotte ||231,139|| ||July 2010 182 New Caledonia ||229,993|| ||July 2010 183 Netherlands Antilles ||228,693|| ||July 2010 184 Vanuatu ||221,552|| ||July 2010 185 Samoa ||192,001|| ||July 2010 186 Sao Tome and Principe ||175,808|| ||July 2010 187 Saint Lucia ||160,922|| ||July 2010 188 Tonga ||122,580|| ||July 2010 189 Virgin Islands ||109,775|| ||July 2010 190 Grenada ||107,818|| ||July 2010 191 Micronesia, Federated States of ||107,154|| ||July 2010 192 Aruba ||104,589|| ||July 2010 193 Saint Vincent and the Grenadines ||104,217|| ||July 2010 194 Kiribati ||99,482|| ||July 2010 195 Jersey ||91,812|| ||July 2010 196 Seychelles ||88,340|| ||July 2010 197 Antigua and Barbuda ||86,754|| ||July 2010 198 Andorra ||84,525|| ||July 2010 199 Isle of Man ||76,913|| ||July 2010 200 Dominica ||72,813|| ||July 2010 201 Bermuda ||68,268|| ||July 2010 202 American Samoa ||66,432|| ||July 2010 203 Marshall Islands ||65,859|| ||July 2010 204 Guernsey ||65,632|| ||July 2010 205 Greenland ||57,637|| ||July 2010 206 Cayman Islands ||50,209|| ||July 2010 207 Saint Kitts and Nevis ||49,898|| ||July 2010 208 Faroe Islands ||49,057|| ||July 2010 209 Northern Mariana Islands ||48,317|| ||July 2010 210 Liechtenstein ||35,002|| ||July 2010 211 San Marino ||31,477|| ||July 2010 212 Monaco ||30,586|| ||July 2010 213 Saint Martin ||30,235|| ||July 2010 214 Gibraltar ||28,877|| ||July 2010 215 British Virgin Islands ||24,939|| ||July 2010 216 Turks and Caicos Islands ||23,528|| ||July 2010 217 Palau ||20,879|| ||July 2010 218 Akrotiri ||15,700|| ||NA 219 Dhekelia ||15,700|| ||NA 220 Wallis and Futuna ||15,343|| ||July 2010 221 Anguilla ||14,764|| ||July 2010 222 Nauru ||14,264|| ||July 2010 223 Cook Islands ||11,488|| ||July 2010 224 Tuvalu ||10,472|| ||July 2010 225 Saint Helena, Ascension, and Tristan da Cunha ||7,670|| ||July 2010 226 Saint Barthelemy ||7,406|| ||July 2010 227 Saint Pierre and Miquelon ||6,010|| ||July 2010 228 Montserrat ||5,118|| ||July 2010 229 Falkland Islands (Islas Malvinas) ||3,140|| ||July 2008 230 Norfolk Island ||2,155|| ||July 2010 231 Svalbard ||2,067|| ||July 2010 232 Christmas Island ||1,402|| ||July 2010 233 Tokelau ||1,400|| ||July 2010 234 Niue ||1,354|| ||July 2010 235 Holy See (Vatican City) ||829|| ||July 2010 236 Cocos (Keeling) Islands ||596|| ||July 2010 237 Pitcairn Islands ||48|| ||July 2010 est.

Mathematica source code of the chart:

In[1]:= <<Graphics`Graphics` In[2]:= list1=Table[{d,100*(Log[10,d+1]-Log[10,d])},{d,1,9}]; In[3]:= Show[{BarChart[{64,43,24,31,15,20,17,11,12}/2.37], ListPlot[list1, PlotStyle\[Rule]PointSize[0.02]]}]
Date
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Author Jakob.scholbach

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