C Program to Calculate Standard Deviation — Full Code & Output

Calculating standard deviation is common in stats. It helps figure out how your data's spread out. If you've got numbers like 2, 4, 4, 4, and 5, you’ll wanna know how much they deviate from the average. This C program takes a list and calculates their standard deviation.

Standard deviation might seem tricky, but it’s super useful. Let’s dive into coding it in C, and you'll get the hang of its application.

Prerequisites for the C Standard Deviation Program

Before diving into the code, ensure you have the following:

• Understanding of arrays in C.
• Familiarity with loops and arithmetic operations.
• Any C compiler such as GCC 9 or newer — or just run it in the EduSeekho online compiler.

Source Code of C Program to Calculate Standard Deviation

Here's the complete C program to calculate the standard deviation for a set of numbers. Follow along with the comments to understand each part.

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

int main() {
    int n, i;
    float sum = 0, sumSq = 0, mean, variance, std_deviation;
    int element[100];

    // Read number of elements
    printf("Enter the number of elements: ");
    scanf("%d", &n);

    // Read elements
    printf("Enter %d elements: ", n);
    for (i = 0; i < n; i++) {
        scanf("%d", &element[i]);
        sum += element[i];
        sumSq += element[i] * element[i];
    }

    // Calculate mean and variance
    mean = sum / n;
    variance = (sumSq / n) - mean * mean;

    // Calculate standard deviation
    std_deviation = sqrt(variance);

    printf("Standard Deviation = %.3f", std_deviation);

    return 0;
}

Output of the Standard Deviation Program

Here's what you can expect when you run the program.

Enter the number of elements: 5
Enter 5 elements: 2 4 4 4 5
Standard Deviation = 1.095

Algorithm to Calculate Standard Deviation in C

Standard deviation tells how much data deviates from the average. This program reads numbers, computes their mean, and calculates the variance, then derives the standard deviation.

1. Read the integer n from the user.
2. Initialize sum and sumSq to zero.
3. For each element, accumulate the sum and sum of squares.
4. Calculate the mean by dividing sum by n.
5. Compute variance using the accumulated sums.
6. Calculate standard deviation as the square root of variance.

flowchart TD
  A([Start]) --> B[/Read n/]
  B --> C[sum = 0, sumSq = 0]
  C --> D{for each element}
  D -->|Yes| E[sum += element[i]]
  E --> F[sumSq += element[i] * element[i]]
  F --> D
  D -->|No| G[mean = sum / n]
  G --> H[variance = (sumSq / n) - mean * mean]
  H --> I[std_deviation = sqrt(variance)]
  I --> J([End])

How the C Program to Calculate Standard Deviation Works

Let's break down how this program calculates standard deviation step by step:

• #include <stdio.h> and #include <math.h> bring in necessary functions for input/output and math operations.
• The program starts by declaring variables like n, sum, sumSq, mean, and storage for elements.
• It reads the number of elements n and then proceeds to read each element into the array element.
• The loop sums up the elements and their squares, updating sum and sumSq.
• Mean is calculated by dividing sum by n, giving the average of numbers.
• The variance is then calculated using (sumSq / n) - mean * mean.
• Finally, sqrt computes the standard deviation from the variance, which is printed out.

Time and Space Complexity of the C Standard Deviation Program

Considering performance, here's how the program fares:

Time Complexity: O(n). n is the number of elements entered by the user—e.g., 5 for five numbers. We loop over all numbers once to calculate the sum and sum of squares. Each additional element requires one more loop cycle.

Space Complexity: O(n). We store the array element of size n, but also use a few additional variables like sum, sumSq, and mean. These variables do not grow with the input size.

Key takeaway:Standard deviation shows how spread out the values in a data set are, and it’s a great tool in data analysis.

FAQs About Calculating Standard Deviation in C

Here are some common questions students have about this program.

Related Programs

If you found this program helpful, check out these related programs:

• C Program to Calculate Simple and Compound Interest
• C Program to Calculate Difference Between Two Time Periods
• C Program to Check Leap Year with Code and Output
• C Program to Find the Area and Perimeter of a Rectangle
• C Program to Calculate Area and Circumference of Circle

Conclusion

Standard deviation’s an important concept in statistics and data analysis. This C program shows you how it's calculated and why it matters. Try playing around with different data sets to get a better feel for its uses.

Test your knowledge with our C programming quiz and run similar programs in our online compiler.