Yesterday I conducted a little experiment. I looked through the foreign
currency exchange data in a national newspaper. There were exchange rates like
2.119 to mean you will need (US dollar) $2.119 to buy £1 sterling. Likewise, you
will need (Euro) ∊1.59 to buy £1 sterling and (Hong Kong dollar) HK $15.390 to
buy £1. Reviewing the results of the data and recording the number of
appearances by first digit, gave the following table:
These results support Benford’s law, which says that for some classes of data,
the number 1 appears as the first digit in about 30% of the data, the number 2
in 18% of the data and so on. It is certainly not the uniform distribution that
occurs in the last digit of the telephone numbers.
It is not obvious why so many data sets do follow Benford’s law. In the 19th
century when Simon Newcomb observed it in the use of mathematical tables he
could hardly have guessed it would be so widespread.
Instances where Benford’s distribution can be detected include scores in
sporting events, stock market data, house numbers, populations of countries,
and the lengths of rivers. The measurement units are unimportant – it does not
matter if the lengths of rivers are measured in metres or miles. Benford’s law has
practical applications. Once it was recognized that accounting information
followed this law, it became easier to detect false information and uncover fraud.
Words
One of G.K. Zipf’s wide interests was the unusual practice of counting words.
It turns out that the ten most popular words appearing in the English language
are the tiny words ranked as shown:
This was found by taking a large sample across a wide range of written work
and just counting words. The most common word was given rank 1, the next
rank 2, and so on. There might be small differences in the popularity stakes if a