Description
The Case Study described in Section 7.6 of our text book describes Benford’s Law:
Benford’s Law involves looking at the first digit of a series of numbers. For
example, suppose that you were to use a random number generator to generate
integers in the range of 100 to 999 and you looked at how often the number
begins with 1, how often it begins with 2, and so on. Any decent random number
generator would spread the answers out evenly among the 9 regions, so we’d
expect to see each digit about one-ninth of the time (11.1%). But with a lot of
real-world data, we see a very different distribution.
Table 7.3 gives the expected distribution under Benford’s Law:
1: 30.1%, 2: 17.6%, 3: 12.5%, 4: 9.7%, 5: 7.9%, 6: 6.7%, 7: 5.8%, 8: 5.1%, 9: 4.6%
You should use this distribution in your program.
You are being provided with a text file giving population data for 247 countries and territories.
Your program should read in the data in this file and extract the information needed to keep
count of how often each first digit is found. It may be useful to know that the ASCII value for the
character ‘1’ is 49.
In addition, you should analyze other publicly available data to see how they test for Benford
analysis. One data repository site where you can find multiple datasets is:
https://archive.ics.uci.edu/ml/datasets.html
For this assignment, you are to design a Java class named Benford that uses an ArrayList object
to store counts of first digits. A Benford object will have only one field, the ArrayList object.
You will need the following class methods (at a minimum – you may add as many helper
methods as you wish):
A constructor to construct Benford objects
A class method named readCounts() that takes a file name as a parameter and that reads
and stores data from a text file into a Benford object.
A class method named benfordPercents() that uses the data in the Benford object to fill
an array of double values giving the percentage counts for each initial digit based on the
raw counts contained in the Benford object.
You are also to design a client class named BenfordPlot that displays the data in the Benford
object graphically. The output should be similar to the examples shown below, except your plot
should be titled “Population of Countries.” The “^” symbol in the plot below indicated the
expected Benford value. The second plot shown below displays a distribution that does NOT
follow Benford’s Law.
The file containing the data you need for this assignment is “popData.txt” – it was obtained from
the website https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_population
A sample of the data file you will be working with is shown below, so that you can see the
format of the data you’ll be using:
The fact that only the population data is numerical may help you parse the data file. Plot the
population data provided to determine whether or not it follows Benford’s Law.
The DrawingPanel.java code is also being provided, in case you do not already have it
downloaded.
Please submit the following files:
Benford.java (your Benford class code) – one per team.
BenfordPlot.java (your client code that using the DrawingPanel code to produce a
graphical display of the data contained in a Benford object) – one per team
Analysis of multiple data sets along with your opinion as to whether or not the data
follow Benford’s Law – one per person
Design and implementation guidelines:
Javadoc comment all class files and methods
Use validation and generate and handle exceptions as appropriate
Structured code – use methods to eliminate redundancy and break large methods into
smaller, logical subproblems