COMP 2100 Project 1: Implementing a statistic class
(20 points)

Due: in lab, Thursday September 3, 2015

You are to implement a Statistic class based on its published specification. You can think of a Statistic object as "an observable random variable" (Wikipedia).A client should be able to use this class to do a number of things: create a named Statistic object, collect a numeric value, retrieve the smallest or largest value collected so far, retrieve the sum, mean (average) or standard deviation of the values collected so far, retrieve a count of the number of values collected, and retrieve its assigned name.

Here is an example of client code that use this class:

  public static void main(String[] args) {
     Statistic scores = new Statistic("quiz scores");
     scores.collect(5);
     scores.collect(7);
     scores.collect(2);
     scores.collect(0);
     scores.collect(1);
     System.out.println( "Number of scores: " + scores.count() );
     System.out.println( "Highest score:    " + scores.highest() );
     System.out.println( "Lowest score:     " + scores.lowest() );
     System.out.println( "Average score:    " + scores.mean() );
  }
  

Number of scores: 5
Highest score:    7.0
Lowest score:     0.0
Average score:    3.0
  

1. Download the project zip file and unzip (right-click, Extract All). It will create a pr1 folder containing
   • StatisticDriver.java, a client class that will thoroughly test your solution.
   • Statistic.java, where you will define your solution. It is an empty class.
   • pr1.gpj, a jGRASP project file.
2. Launch jGRASP and from the Project menu, select Open. A dialog will appear. Browse to your pr1 folder and select pr1.gpj.
3. Notice that an Open Projects section is displayed in the Browse tab (left center of the screen). I have already created a Project file and added both StatisticDriver.java and Statistic.java to the project. They are listed here and you can open them from here.
   
4. Open Statistic.java and implement the methods as specified. I recommend that you start by writing the methods as stubs. This means they will have their correct return type and parameters, they will compile, but they will not do anything. For void methods (commands), the method body will be empty - nothing between the curly brackets. For methods that return a value (questions), the method body will have to contain a return statement that returns a dummy value of the expected type - e.g. return 0.0; if the return type is double.
5. You need to decide what instance variables will be needed to implement these methods, and add them to the class definition. They should of course be private.
6. Do NOT store every collected value, such as in an array. You don't know how many there will be. All methods, including standard deviation, can be implemented without storing individual collected values. Explanations follow.
7. Given a collection X of values x₁, x₂, ..., x_n, the mean is defined as (Σ x_i)/n. Think about how you can calculate this without having to keep all the x_i.
8. The standard deviation of a population of values is defined as the square root of the variance of that collection. Variance is defined as the average squared deviation from the mean. The formula to calculate variance can be given as: (Σ x_i²)/n - ((Σ x_i)/n)², where x_i are individual values collected and n is the number of values collected. For example, if you collected the values 1, 2, 3, 4, 5, then (Σ x_i²)/n = (1+4+9+16+25)/5 = 55/5 = 11, and ((Σ x_i)/n)² = ((1+2+3+4+5)/5)² = (15/5) ² = 3² = 9, so the variance is 11-9 = 2. The standard deviation is the square root of this, which for this example is 1.414.
9. Due to inaccuracies in computation with floating point numbers, operations on the Java double data type do not throw exceptions (for such conditions as zero divide); they instead produce a special constant result called Double.NaN. In the situation where no values have been collected yet, count() should return 0 and sum() should return 0.0, but the others (highest, lowest, current, mean, standardDeviation) should return Double.NaN.
10. Best Solution Approach: Do all calculations and update instance variables in the collect method, since this is where a new value comes in. By doing so, the other methods (highest, lowest, etc) can just return the updated value of the appropriate instance variable.
11. In addition to all this, document your code using Javadoc-style comments. Such comments should go at the top of the class and before each method. Your methods should use the @param and @return tags as appropriate.
12. With the Project open (see items 2 and 3 above), you can select the Documentation icon (the open book) -- or Generate Documentation from the Project menu -- to generate web pages from the Javadoc. A dialog will appear.
    
    Uncheck the "Include private items" box, and click Generate. jGRASP will create a folder called pr1_doc in with your other files, and generate all the web pages into that folder. A browser window should pop up with the index.html page displayed. Every class in the project is included, so to see the Statistic web page click its name in the upper left.
13. If the previous step fails, and it probably will, refer to the document Generating an API webpage from a Java source file with Javadoc-style comments for instructions on generating the API using a Windows command prompt.

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