# 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

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

## 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 −

#include <math.h>
#define MAXSIZE 100
main( ) {
int i,n;
float value [MAXSIZE], deviation,
sum,sumsqr,mean,variance,stddeviation;
sum = sumsqr = n = 0 ;
printf("Input values: input -1 to end ");
for (i=1; i< MAXSIZE ; i++) {
scanf("%f", &value[i]);
if (value[i] == -1)
break;
sum += value[i];
n += 1;
}
mean = sum/(float)n;
for (i = 1 ; i<= n; i++) {
deviation = value[i] - mean;
sumsqr += deviation * deviation;
}
variance = sumsqr/(float)n ;
stddeviation = sqrt(variance) ;
printf("Number of items : %d",n);
printf("Mean : %f", mean);
printf("Standard deviation : %f", stddeviation);
}

## Output

When the above program is executed, it produces the following output −

Input values: input -1 to end
2 4 6 8 12 4.5 6.7 0.3 2.4 -1
Number of items: 9
Mean: 5.100000
Standard deviation: 3.348300

Updated on: 25-Mar-2021

5K+ Views