/*****************************************************/
/* File: loop_exercise.c                             */
/* Author: Prof. Marron                              */
/* Date: March 26, 2014                              */
/* Description:                                      */
/*   Computes the mean, variance, and std. deviation */ 
/*   of a list of numbers.  The user is prompted to  */
/*   enter the number of data items (n) and then is  */
/*   prompted to enter each item.  Once all items    */
/*   have been entered, computes the mean, variance, */
/*   and standard deviation and prints them out.     */
/*                                                   */
/* Compile with gcc -Wall loop_exercise.c -lm        */
/*****************************************************/     

#include <stdio.h>
#include <math.h>

int main() {
    int i;		/* loop variable             */
    int n;		/* number of data items      */
    float data;		/* data item                 */
    float sumx; 	/* sum of data items         */
    float sumx2;	/* sum of squared data items */
    float mean;		/* mean of the data          */
    float var; 		/* variance of the data      */
    float sd;		/* std. deviation of data    */

    /* Get the number of data items from the user */

    printf("How many numbers do you need to enter (n)? ");
    scanf("%d", &n);

    /* EXERCISE 1                                          */
    /* The number of data items (n) must be positive.      */
    /* Use a while loop to ensure that the user enters     */
    /* a positive value.                                   */
    
    /* Initialization */

    sumx = sumx2 = 0.0;

    /* Prompt the user to enter the data; compute the sum  */
    /* of the numbers and the sum of the squares of the    */
    /* numbers.                                            */

    i = 1;
    while (i <= n) {
        printf("Enter data item %d: ", i);
        scanf("%f", &data);

        sumx = sumx + data;
        sumx2 = sumx2 + (data*data);

        i = i + 1;
    }

    /* EXERCISE 2                                         */
    /* The while loop above is counter-controlled and can */
    /* be implemented more succinctly as a for loop.      */
    /* Re-write the loop as a for loop.                   */

    /* EXERCISE 3                                         */
    /* Modify the program so that it also computes and    */
    /* prints the maximum and minimum values entered.     */

    /* Compute the mean, variance, and std. deviation     */

    mean = sumx / n;
    var = 1.0/(n-1) * (sumx2 - (1.0/n)*sumx*sumx);
    sd = sqrt(var);

    /* print the computed values */

    printf("\n");
    printf("     mean = %f\n", mean);
    printf(" variance = %f\n", var);
    printf("std. dev. = %f\n\n", sd);
}