/* --------------------------------------------------------------------- 
**  Figure 10.15:  Mean and standard deviation.
**  Figure 10.17:  The get_data() function.
**  Figure 10.18:  Functions average() and variance().
** --------------------------------------------------------------------- 
*/
#include "tools.h"                                                                                   

#define N     50            /* number of data values  */
void   get_data( double x[], int n );
double average ( double x[], int n );
double variance( double x[], int n, double mean );
    
void main( void )                                  
{   
    double x[N];    /* An array for the N data values. */
    int num;        /* Actual number of data values. */ 
    double mean;    /* The mean of the values in array x. */ 
    double var;     /* Variance of the data in array x. */ 
    double stdev;   /* Standard deviation of the data in array x. */ 

    banner();

    printf( "\n Enter number of values in data set (2..%i): ", N );
    for (;;) {
        scanf( "%i", &num );
        if (num > 1 && num <= N) break; 
        printf( "Error: %i is out of legal range, try again: \n", num );
    }
    printf( " Computing statistics on %i data values.\n", num );

    get_data ( x, num );
    mean = average( x, num );                                
    var = variance( x, num, mean );                                       
    stdev = sqrt(var);

    printf( "\n\n The mean of the %i data values is = %.2f \n", num, mean );  
    printf( "\n The variance is = %.2f \n", var );                          
    printf( "\n The standard deviation is = %.2f \n", stdev );
    bye();
}

/* -----------------------------------------------------------------   
// Given an empty array of length n, input data values to fill it.
*/
void 
get_data( double x[], int n )
{   
    int k;                      /* Loop counter and array subscript. */

    puts( " Please enter data values when prompted." );
    for (k = 0; k < n; ++k) {
        printf( " x[%i] = ", k );       /* Prompt for kth value. */
        scanf( "%lg", &x[k] );          /* Read into array slot k. */
    }
}          

/* -----------------------------------------------------------------   
// Given an array of values, print the values and calculate the mean.
*/
double 
average( double x[], int n )
{   
    double sum; 
    int k;                      /* Loop counter and array subscript. */

    for (sum = k = 0; k < n; ++k) {
        printf( "\n    x[%d] = %.2f", k, x[k] );
        sum += x[k]; 
    }           
    return sum / n;
}

/* -----------------------------------------------------------------   
// Given an array of values and their mean, calculate the variance.
*/
double 
variance( double x[], int n, double mean ) 
{   
    double divisor, sum;
    int k; 

    for (sum = k = 0; k < n; ++k) {     /* Compute and sum the k-squares. */
        sum += pow( (x[k]-mean), 2 );
    }
    if (n < 20) divisor = n-1;  
    else divisor = n;  
    return sum / divisor;
}