Write a program that takes its input from a binary file of numbers of type double. The file contains nothing but numbers of type double written to the file with writeDouble. The program outputs to the screen the average and standard devia- tion of the numbers in the file. 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. Hint: Write your program so that it first reads the entire file and computes the average of all the numbers, then closes the file, and then reopens the file and computes the standard deviation.