/*
 * This program reads numbers into an array from a file called "numbers", o
 * then prints the average and standard deviations of the numbers.
 */
#include <stdio.h>
#include <math.h>

#define MAX_NUMBERS	1000

/* This function reads the numbers from the file "numbers", returning
 * with the numbers of items read
 */
int read_numbers (float v[]) {
	int	i;
	float	num;
	FILE	*fp;

	/* open the file */

	fp = fopen ("numbers", "r");

	/* fp is NULL?  complain. */

	if (!fp) {
		fprintf (stderr, "read_numbers: can't open file!\n");
		exit (1);
	}

	/* loop until break */

	for (i=0;;) {

		/* read an item */

		fscanf (fp, "%f", &num);

		/* end of file?  break. */

		if (feof (fp)) break;

		/* too many numbers?  uh-oh... */

		if (i >= MAX_NUMBERS) {
			fprintf (stderr, "read_numbers: too many numbers!\n");
			exit (1);
		}

		/* put the number into the array, then increment the index */

		v[i++] = num;
	}
	fclose (fp);

	/* i is the number of items read */

	return i;
}

/* this function finds the arithmetic mean of numbers in an array */

float find_average (float v[], int n) {
	int	i;
	float	sum;

	/* can't divide by zero... */

	if (n < 1) {
		fprintf (stderr, "find_average: too few numbers!\n");
		exit (1);
	}

	/* find total of numbers */

	sum = 0;
	for (i=0; i<n; i++) sum += v[i];

	/* return, dividing by n */

	return sum / n;
}

/* This function finds the standard deviation of numbers in an array,
 * given their average 
 */

float find_sd (float v[], int n, float avg) {
	int	i;
	float	sumsq, dif;

	/* can't have undefined or infinite variance */

	if (n < 2) {
		fprintf (stderr, "find_sd: too few numbers!\n");
		exit (1);
	}

	/* find the total of the squared differences from the average */

	sumsq = 0;
	for (i=0; i<n; i++) {
		dif = v[i] - avg;
		sumsq += dif * dif;
	}

	/* return standard deviation */

	return sqrt (sumsq / (n-1));
}

/* main program */

int main () {
	float	avg, 			/* the average */
		sd, 			/* the standard deviation */
		nums[MAX_NUMBERS];	/* the array of numbers */
	int	n;			/* number of items in array */

	/* read the numbers */

	n = read_numbers (nums);

	/* find the average */

	avg = find_average (nums, n);

	/* find the deviation */

	sd = find_sd (nums, n, avg);

	/* print the results */

	printf ("average = %f, sd = %f\n", avg, sd);

	/* bye! */

	exit (0);
}