Write a program that takes its input from a file of numbers of type double. The program ou...

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:

The number a is the average of the numbers n1, n2, n3, and so forth.

Hint: Write your program so that it first reads the entire file and computes the average of all the numbers, then closes the file, then reopens the file and computes the standard deviation. You will find it helpful to first do Programming Project 12.2 and then modify that program to obtain the program for this project.