Chapter 6, Problem 4P

Write a program that takes its input from a file of numbers of type double. The program outputs to the screen the average and standard deviation of the numbers in the file. The file contains nothing but numbers of type double separated by blanks and/or line breaks. The standard deviation of a list of numbers n₁, n₂, n₃, and so forth is defined as the square root of the average of the following numbers:

  (n₁ – a)², (n₂ – a)², (n₃ – a)² and so forth

The number a is the average of the numbers n₁ n₂, n₃, and so forth. If this is being done as a class assignment, obtain the file name from your instructor. (Hint: Write your program so that it first reads the entire file and computes the average of all the numbers, and then doses the file, then reopens the file and computes the standard deviation.)