Statistics

Background:

1. A text file, (numbers.txt), containing a large (N <= 1000) number of integers is included in the folder you snarf from Web-CAT. The integers range in value from 0 to 100. The text file has been created with one value on each line. Due to the potential for the sum of the numbers to be very large, you should use a long integer in your calculation to find the average.

2. The number of integers in the file is unknown.

3. Your program must find the average, standard deviation, and mode of the list of numbers. The mode is defined as the value(s) present with the highest frequency. Calculating the standard deviation consists of the following steps:

   1. Find the average of the list of numbers.
   2. Determine the difference of each number from the average, and square each difference. Sum all the differences.
   3. Divide this sum by (the number of values - 1).
   4. Take the square root of the above division result from step c.
   
   

4. Example, given this list of numbers: 7 4 5 9 10

   1. The average = 7
   2. Sum of square of differences:

      

   3. 
   4. 
   
   

5. For a normal distribution, 68.3% of the data will lie within one standard deviation of the average, while 95.4% will lie within two standard deviations.

Assignment:

1. Your program should print out the average, standard deviation, and mode of the data in numbers.txt.

2. Your program must utilize proper modular design and parameter passing. Instead of doing all calculations in one function, create and utilize various helper functions that are useful for your calculations.

3. Turn in your source code and run output.

Tips:

1. In VS-Code, make sure you open ONLY the folder for Statistics (not the entire workspace with all your other lab folders). VS-Code will not be able to run and open the file called numbers.txt unless you only have the Statistic folder open.

2. Be sure to look at the fields in the Statistics.java. Specifically, what is the meaning of howMany? DO NOT START THIS UNTIL YOU HAVE ANSWERED THIS IMPORTANT QUESTION.

3. The numbers.txt file is big and has a lot of numbers. It is really not a super useful file for testing your code. Make a new file - like mynumbers.txt - and put a small set of numbers - like 4 numbers or 10 numbers. You can then use this to test out the average, standard deviation and mode methods more easily.