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ITECH1400 - Programming

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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 5 June 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 (document

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Introduction

Benford’s law, also known as Benford-Newcomb’s law is a law of anomalous numbers. It is about the pattern followed by the distributions of leading digits in numbers. The law states that the frequency distribution of the leading digits follows the following formula:

 

The values we get after applying the formula on all the digits are plotted below:

 

Figure 1: Predicted Benford's law frequencies

Our goal is to investigate the application of this law in two data set, specifically in the Fibonacci series and the length of rivers in the world.

The Fibonacci series begins with two numbers 1 and 1 and these two numbers are added to continue the series giving rise to an interesting series.

Methodology

In order to implement and test the law we used Microsoft Excel and Python. With these tools we can easily generate the Fibonacci series up to any numbers. First we used Excel to generate the Fibonacci series up to 24 terms and we calculated the frequency of the leading digits. Then Chi-square test for goodness of fit is used to test the law. Then we repeated the same for the first 50 terms of Fibonacci series. We also recreated this study using Python. In order to implement this in python the following pseudocode is used.

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