, but did notBENFORD’S LAW ASSIGNMENT
Many years ago ( B.C. – before calculators ) it was noted by
mathematician Simon Newcomb, while using log tables, that the pages near the
start were much more worn than the pages near the end. For some reason, it seems
most of the numbers being converted to logs started with the digit 1, then, to a
lesser extent, the digit 2, and so on, with the digit 9 being used the least. He
proposed that the digit n in a list of number should occur as the first digit
with a frequency of
, but did not
investigate it further. In 1938 physicist Frank Benford rediscovered this relation and then analyzed several sets of data to verify the relation. He published his results and thus the relation became known as Benford’s Law.
For example, the distribution chart below was generated from a list of the populations of 197 countries.
|
first digit |
actual count |
actual occurrence |
theoretical distribution |
|
1 |
56 |
28% |
30% |
|
2 |
31 |
16% |
18% |
|
3 |
25 |
13% |
12% |
|
4 |
23 |
12% |
10% |
|
5 |
22 |
11% |
8% |
|
6 |
11 |
6% |
7% |
|
6 |
14 |
7% |
6% |
|
8 |
10 |
5% |
5% |
|
9 |
5 |
3% |
5% |
ASSIGNMENT
For each of the following, create a table as above, a corresponding graph ( what type is best ? ) and a conclusion as to whether the data fit Benford’s Law.
· a list of 200 random numbers between 0 and 10000
· a list of the powers of 3 up to limitations of calculation
· 2 lists of at least 150 numbers, random data obtained from a print source or the internet. GO BACK