The challenge for this month’s Exercise is to calculate the standard deviation for a given set of data points. It’s a “whole population calculation” because all the data points are present. The trick is to follow the equation, transforming it from cryptic math mumbo-jumbo into C code.

Figure 1 shows the equation I used, which follows these steps:

Figure 1. The mathematical monster used to calculate standard deviation (full set).

1. Calculate the mean for the values, what I would normally call the “average.” Tally up all the data points and divide by the number of data points.
2. Subtract the mean from each element in the data set and square the result. These values are totaled to obtain their mean. The result is the variance.
3. Obtain the square root of the variance to get the standard deviation.

The sample code skeleton provided in the Exercise post listed the values[] array as the data set. Variable items is set to the number of items in the data set: items = sizeof(values)/sizeof(int); These two variables are passed to the stddev() function where they’re manipulated to calculate and return the standard deviation.

Here’s my solution, which follows the steps outlined above:

2024_05-Exercise.c

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

/* whole population calculation */
double stddev(int v[],int items)
{
    int x,total;
    double mean,variance;

    /* calculate sum */
    total = 0;
    for( x=0; x<items; x++ )
        total += v[x];

    /* calculate the mean (average) */
    mean = (double)total/items;

    /* calculate deviations */
    total = 0;
    for( x=0; x<items; x++ )
        total += (v[x]-mean)*(v[x]-mean);
    variance = (double)total/items;

    return( sqrt(variance) );
}

int main()
{
    int values[] = { 10, 12, 23, 23, 16, 23, 21, 16 };
    int x,items;

    /* output the array's values */
    items = sizeof(values)/sizeof(int);
    printf("Values:");
    for( x=0; x<items; x++ )
    {
        printf(" %2d",values[x]);
    }
    putchar('\n');

    printf("The standard deviation is %.4f\n",
            stddev(values,items)
          );

    return 0;
}

The first for loop in the stddev() function obtains the total of all values in the data set, v[]. The mean is calculated: mean = (double)total/items; The double cast is required as mean is a double variable.

The next for loop calculates the deviation: Variable total tallies the squares of the difference between each value v[x] and the mean: total += (v[x]-mean)*(v[x]-mean); The multiplication expression squares the values, which is my preferred method over using the pow() function.

Variable variance is assigned the value of the total of the squares divided by the number of items.

Finally, the return statement returns the square root of variable variance, which is the whole population standard deviation value. Remember to link in the math library to assist with the sqrt() function.

Here’s a sample run:

Values: 10 12 23 23 16 23 21 16
The standard deviation is 4.8990

I checked my solution’s result with the standard deviation calculated by ChatGPT on the same data set and received the same value. So I think I’m good. I hope you’re solution also met met with success and that you didn’t use ChatGPT to write it for you.