//
// Program name:  variance
// Author:  B. Massingill 
//
// Purpose:  compute the variance of a sequence of numbers
//
// Input:  
//	a sequence of floating-point numbers x(0), x(1), .... x(n-1)
//		read from standard input, terminated by end-of-file
//		(control-D if entered from keyboard)
//	(here, x(i) means "x-subscript-i")
// Output:  
//	the variance of (x(0), x(1), ... x(n-1)) -- which is the sum,
//		for 0 <= i <= n-1, of (x(i) - avg) squared, where
//		avg is the average of the x(i)'s
//	for example,
//		for input 1 2 3 4, the program should compute and
//		print ...
//	(written to standard output)
//
// The program assumes that n <= 20.  If the user enters more than
//	20 numbers, the program will print a warning message and
//	perform the calculation using the first 20 numbers.
//
#include <iostream.h>
int main()
{
	const int MAXNUMS = 20 ;	// maximum number of inputs
	// note the use of a "const" (constant) integer here.
	// we use MAXNUMS anywhere we need the maximum number of
	// inputs.  so if we later decide to increase it to 100,
	// we don't go through the program and look for all the 20s,
	// we just change the above line.

	double x[MAXNUMS] ;		// inputs x(i)
	int n = 0 ;			// number of inputs so far
	double sum = 0.0 ;		// sum of inputs so far

	// prompt user
	cout << "Enter numbers, control-D to end\n" ;

	// read while there is input and not too many numbers:
	//	x[n] is always the "next" spot in the array
	//	if n >= MAXNUMS, exit the loop (no more room in array)
	//	otherwise if there is no more to read, exit the loop
	//		("cin >> x[N]" reads input and also returns true
	//		if there was something to read, false if not)
	while (n < MAXNUMS && cin >> x[n])
	{
		// increment running total, count
		sum += x[n] ;
		n++ ;

		// 
	}
	// if n >= MAXNUMS, the user entered at least MAXNUMS numbers,
	//	and we read MAXNUMS of them
	// so we want to try to read one more to see whether to print
	//	a warning message
	// we need a place to read into, but we don't need to use the
	//	value read (if any) -- so read into xtemp
	double xtemp ;			
	if (n >= MAXNUMS)
	{
		if (cin >> xtemp)
			cout << "Warning:  More than " << MAXNUMS <<
				" numbers entered.  Only the first " <<
				MAXNUMS << " will be used.\n" ;
	}

	// now compute the average
	double avg ;
	if (n > 0) 
		avg = sum / n ;

	// and now compute the variance 
	// note that this will work even if n == 0! 
	int i = 0 ;
	double variance = 0.0 ;	
	while (i < n)
	{
		variance += (x[i] - avg) * (x[i] - avg) ;
		i++ ;
	}

	if (n > 0)
		cout << "Variance is " << variance << endl ;
	else
		cout << "No numbers entered\n" ;

	return 0 ;
	
}