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Python代写 | ITECH1400 Foundations of Programming

这个作业是用Python编写一个应用程序,将Benford’s Law应用于给定的一组数据
ITECH1400 Foundations of Programming
Logarithms, Benford’s Law and
Fraudulent Data
Overview
In this assignment you will write an application in Python that will apply Benford’s Law to
a given set of your own data. This is an individual assignment.
Timelines and Expectations
Percentage Value of Task: 20%
Due: Friday 29 May 2020 @17:00 (week 11)
Minimum time expectation: 20 hours
Learning Outcomes Assessed
The following course learning outcomes are assessed by completing this assessment:
K1. Identify and use the correct syntax of a common programming language.
K2. Recall and use typical programming constructs to design and implement simple software
solutions.
K3. Reproduce and adapt commonly used basic algorithms.
K4. Explain the importance of programming style concepts (documentation, mnemonic names,
indentation)
S2. Write and implement a solution algorithm using basic programming constructs.
S3. Demonstrate debugging and testing skills whilst writing code.
A1. Develop self-reliance and judgement in adapting algorithms to diverse contexts.
A2. Design and write program solutions to identified problems using accepted design constructs.
Assessment Details
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 2
Background
At the turn of the century, if
you wanted to do some
serious calculating you usually
used a book of logarithms1
to
help you do the arithmetic; the
pages in the book of
logarithms were arranged in
numerical order.
A sample logarithms page,
from the link below, is shown
here on the right.
An astronomer, Simon
Newcomb, noticed that the
pages at the beginning of the
book were much more worn
than those at the back of the
book – which were hardly used
at all – much like that shown in
the picture of a well-thumbed
book below.
Newcomb noticed that the
leading digits, of all the
numbers used in his
calculations, were more likely
to be small digits rather than
large digits.
Newcomb published a note2
about this and nothing more
was heard about it – this was
in1881.
Intuitively most people still felt that the digits
1 – 9 were evenly distributed in all numbers.
However, in 1937, a physicist by the name of
Frank Benford, discovered Newcomb’s idea
and set about testing this idea using over
20,000 different sets of data such as: lengths
of rivers, street addresses, death rates,

1 https://www.wikiwand.com/en/Common_logarithm
2 Newcomb, S. (1881). Note on the Frequency of Use of the Different Digits in Natural Numbers. American
Journal of Mathematics, 4(1), 39-40.
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 3
sports statistics, molecular weights and so on – and it is base and scale invariant – the length
of rivers could be in miles, kilometres, metres or even cubits.
Theory
Although you do not need to know the derivation3 or proof of Benford’s law, all you need to
know is how to apply it to a set of data.
Benford’s law states4
:
1
1
1 1 10 1 Pr( ) log (1 ) d {1,2,…,9} D d d
    (Equation 1)
So that, for the first digit in a number, the probability that this digit is a ‘1’ is:
or about 30.1%.
Similarly for the remaining digits 2-9.
If we do this for all the digits and plot them as a bar graph, we get:

3 See, for example, Miller, S. J. (2015). A Quick Introduction to Benford’s Law. In S. J. Miller (Ed.), Benford’s
Law (pp. 3-22): Princeton University Press.
4 Nigrini, M. J., & ProQuest (Firm). (2012). Benford’s law applications for forensic accounting, auditing, and
fraud detection, Wiley corporate F & A, p.5
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 4
Your Task
Develop a Python program which will load up a set of data, determine the frequencies of the
leading digits and compare them with the predicted distribution of Benford’s law. Display this in
a bar chart and a table of values. For example:
Digit 1: Observed = 0.321 Expected = 0.301
Digit 2: Observed = 0.153 Expected = 0.176 and so on up till digit 9.
We shall look at three cases.
An Excel spreadsheet has been taken from Office-Watch: Benford’s Law and Excel5
to let you
quickly visualize the Python application that we need make.
Case 1 – Fibonacci series6
This series begins with two numbers 1,1 – these two numbers are added to continue the
series giving rise to the following (only the first 8 terms of the series are shown here):
1,1,2,3,5,8,13,21,. . .
There are many examples of this pattern in Nature and the series is closely related to the
Golden7
ratio.
Using the Excel spreadsheet generate a Fibonacci series up to the 24th term and see if the first
digits obey Benford’s Law. Does it get better if you add more terms?
The Chi-test8 measures how close an actual value is to the expected value – the closer it is to
100% the closer the actual value is to the expected value. In our case, we are testing how
close the frequency of each digit in our dataset is to Benford’s prediction for that digit.
What is the value of the ChiTest comparison for this Fibonacci series? Does it get better if we
add more terms to the series?
Case 2 – Fibonacci numbers & Benford’s law using Python
In this case you are to repeat the analysis in Case 1 but using you Python code.

5 https://office-watch.com/2012/benfords-law-and-excel/
6 https://en.wikipedia.org/wiki/Fibonacci_number
7 https://en.wikipedia.org/wiki/Golden_ratio
8 Also written as 2
 -test
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 5
Case 3 – Length of Rivers9
in the World
In this case, use your Python code to see whether the lengths of rivers in the world follow
Benford’s law.
Fraud detection using Benford’s Law
One use of Benford’s Law is to detect cases of Fraud. Consider the 1993 case of State of Arizona v Nelson.
The accused diverted nearly $2M to fake vendors in an attempt to defraud the State. The frequency of first
digits in the written cheques clearly violates Benford’s Law leading to a conviction.
Another case is that of Enron in its posting of revenue for the year 2000. Comparison of the
frequency of first digits versus the expected frequency shows large discrepancies. The
company went bankrupt the following year – one of the greatest financial failures in history.

9 https://en.wikipedia.org/wiki/List_of_rivers_by_length
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 6
Submission
A report is to be submitted in this assignment. There is a discussion section in the report in which you can
apply step 6 in the six-step problem solving process and ask the four questions often used in evaluating a
solution.
More details on academic reports are available – please refer to this link:
https://federation.edu.au/current-students/learning-and-study/online-help-with/guides-to-yourassessments
There are three important parts at the link above:
1. General Guide to Writing and Study Skills
This section describes the content of a report – refer to page 34 – Abstract, Table of Contents,
Introduction and Conclusion and so on.
2. General Guide to Referencing
APA referencing style is described in this section – EndNote is also available to students
3. Assignment Layout and Appearance Guidelines
This section describes how the report should appear: margin sizes, fonts, how diagrams and
tables are presented and so on.
You must supply your program source code files and your documentation, together with any files required
to run your application, as a single zip file named as follows:
_.zip
e.g. Ada_LOVELACE_30331815.zip
You may supply your word processed documentation in either Microsoft Word or LibreOffice/OpenOffice
formats only – no proprietary Mac specific formats, please.
Assignments will be marked on the basis of fulfilment of the requirements and the quality of the work.
In addition to the marking criteria, marks may be deducted for failure to comply with the assignment
requirements, including (but not limited to):
• Incomplete implementation(s), and
• Incomplete submissions (e.g. missing files), and
• Poor spelling and grammar.
You might be asked to demonstrate and explain your work.
CRICOS Provider No. 00103D 1400 Assig 2, 2020-05 7
Marking Criteria/Rubric
Task Mark
1 Pseudo-code for all Python scripts 10
2
Final Python code (Exceptions 2 marks), annotated with author details and
with comments throughout the code (2 marks), consistent with pseudo-code
10
3 Tests to check that Python code is working correctly 10
4 Case 1 – Fibonacci numbers using example Excel sheet 5
5
Case 2 – Fibonacci numbers using your Python script – bar chart (10) & table
(5)
15
6
Case 3 – Lengths of Rivers using your Python script – bar chart (10) & table
(5)
15
7 Discussion (including 4 Questions in Step 6) 15
8
Report: Abstract, Title Page, Table of Contents (including Figures & Tables),
Introduction, Method, Results, Discussion (including the 4 Questions in Step
6 of problem solving), Acknowledgements & Statement of Authorship,
References
20
TOTAL 100
Final Grade /20
Feedback
Ongoing feedback will be given in lectures and labs/tutes online classes and in arranged
meeting. Feedback will also be given in Moodle.
Plagiarism
Plagiarism is the presentation of the expressed thought or work of another person as
though it is one’s own without properly acknowledging that person. You must not allow
other students to copy your work and must take care to safeguard against this
happening. More information about the plagiarism policy and procedure for the
university can be found at http://federation.edu.au/students/learning-and-study/online-helpwith/plagiarism.


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