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Benfords law (first-digit law)

Benfords Law

This will be one of the world most unexplained phenomena you would ever see. The miracle of numbers that occurs in a set of natural data was discovered by Benford in 1938 and later referred by his name.

Benford observed that 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently: 9 as the first digit less than 5% of the time on most of real-life sources of data. But still astounding fact is nobody can bring out a valid reason behind this occurrence.

Consider any set of naturally occurring numbers. It can be an electricity bills of people in a state, population statistics, stock values, death rates in the world by countries or standard number sets like Fibonacci Series, Factorials and Powers of two.

Example:

Lets look for the 1st 30 numbers in the Fibonacci series.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229.

In this above example,

1 as first digit comes 9 times. ie 30%

9 as first digit comes just 1 times. ie 3%

Real Life Example 1:

In the below link, listed out the statistical data of oil consumed by the top 208 countries.

Check here for stats: World Oil Consumption Statistics by Country

1 as first digit comes 71 times, ie, 34%

2 as first digit comes 41 times, ie 19%

3 as first digit comes 25 times, ie 12%

4 as first digit comes 15 times, ie 7%

5 as first digit comes 12 times, ie 5%

6 as first digit comes 5 times, ie 2%

7 as first digit comes 13 times, ie 6%

8 as first digit comes 8 times, ie 3%

9 as first digit comes 10 times, ie 4%

Real Life Example 2:

Lets take the statistical data of world internet users of top 212 countries.

Check here for stats: World Internet Users Statistics by Country

1 as first digit comes 66 times, ie, 31%

2 as first digit comes 39 times, ie 18%

3 as first digit comes 31 times, ie 15%

4 as first digit comes 23 times, ie 10%

5 as first digit comes 15 times, ie 7%

6 as first digit comes 11 times, ie 5%

7 as first digit comes 14 times, ie 6%

8 as first digit comes 4 times, ie 1%

9 as first digit comes 6 times, ie 3%

In the above real life sources of data, you can find one as the first digit holding more than 30percent while 9 occurs as the first digit is less than 5percent.

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