C program to calculate the standard deviation

Standard deviation is used to measure deviation of data from its mean. The mathematical formula to calculate the standard deviation is as follows −

$$s=\sqrt{Variance}$$

where

Variance$$=\frac{1}{n}\:\:\displaystyle\sum\limits_{i=1}^n (x_{i}-m)^{2}$$

and

$$m=mean=\frac{1}{n}\:\displaystyle\sum\limits_{i=1}^n x_{i}$$

Syntax

#include <math.h>
double sqrt(double x);

Algorithm

Refer an algorithm given below to calculate the standard deviation for the given numbers −

• Step 1 − Read n items.
• Step 2 − Calculate sum and mean of the items.
• Step 3 − Calculate variance.
• Step 4 − Calculate standard deviation.

The logic used in the program for calculating standard deviation is as follows −

for (i = 1 ; i<= n; i++){
   deviation = value[i] - mean;
   sumsqr += deviation * deviation;
}
variance = sumsqr/(float)n ;
stddeviation = sqrt(variance) ;

Example

Following is the C program to calculate the standard deviation for the given numbers −

Note: Since this program requires interactive input, use predefined values for online execution.

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

int main() {
    int i, n = 9;
    float value[] = {2, 4, 6, 8, 12, 4.5, 6.7, 0.3, 2.4};
    float deviation, sum, sumsqr, mean, variance, stddeviation;
    
    sum = sumsqr = 0;
    
    // Calculate sum
    for (i = 0; i < n; i++) {
        sum += value[i];
    }
    
    // Calculate mean
    mean = sum / (float)n;
    
    // Calculate sum of squared deviations
    for (i = 0; i < n; i++) {
        deviation = value[i] - mean;
        sumsqr += deviation * deviation;
    }
    
    // Calculate variance and standard deviation
    variance = sumsqr / (float)n;
    stddeviation = sqrt(variance);
    
    printf("Number of items: %d<br>", n);
    printf("Mean: %.6f<br>", mean);
    printf("Variance: %.6f<br>", variance);
    printf("Standard deviation: %.6f<br>", stddeviation);
    
    return 0;
}

Output

Number of items: 9
Mean: 5.100000
Variance: 11.210000
Standard deviation: 3.348300

Key Points

• Include <math.h> header for the sqrt() function.
• Standard deviation is the square root of variance.
• Use proper array indexing starting from 0 to avoid undefined behavior.
• Cast to float when dividing integers to get precise decimal results.

Conclusion

Standard deviation calculation in C involves computing the mean, finding squared deviations, calculating variance, and taking the square root. This statistical measure helps understand data spread and variability.