# C Program to find the mean, variance and standard deviation

May 1, 2022, Learn eTutorial
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## What is Mean?

Mean: it is the average of all elements in a set of values. Mean add the values in a set and divide the sum with the number of elements. For example, if a set has 3 numbers [1,2,3] then the mean is calculated using 1+2+3 = 6/3 =2.

## What is a Variance?

Variance: it is the average of the squared difference between the mean and the values of the data set. It is called the spread of data within a sample of data.

## What is Standard deviation?

Standard deviation: after we found the variance, we can calculate the standard deviation by taking the square root of the variance.

In this C program, we take the values and save that in an array. The mean calculation is done by taking the average of the sum by using a `for loop`. After that, we need to calculate variance using the formula.

`````` v_sum = v_sum + pow((nums[i] - avrg),2);
var = v_sum / (float) n; ```
```

After calculating the variance, it is easy to find the standard deviation. for that, we use the sd = sqrt(var) formula. Finally, we have to display the results using `printf`.

### ALGORITHM

STEP 1: Include the Header files into the C program to use the built-in functions.

STEP 2: Define and initialize the Array and the variables.

STEP 3: Accept the value for the number of terms from the user using `printf` and `scanf` functions.

STEP 4: Accept the numbers from the user and add those numbers into an Array using `for loop` and `scanf`.

STEP 5: Open a `for loop` from i=0 to the number of terms n to calculate the mean. Add each element and save it in sum, and divide sum with the number of terms.

STEP 6: Open another `for loop` from i=0 to n to find the variance. In each iteration of loop calculate,

v_sum = v_sum + pow((nums[i] - mean),2) , and after that use the formula var = v_sum / (float) n

STEP 8: Calculate the Standard deviation sd by taking the square root of var.

STEP 10: print the mean, sd, and var using `printf`.

## C Source Code

```                                          ```#include <stdio.h>
#include <math.h>
#define MAXSIZE 10

void main()
{

float nums[MAXSIZE];
int  i, n;
float mean, var, sd, sum=0, v_sum=0;   /* declares the variables*/
printf("Enter the number of elements\n");   /* accepts values from user */
scanf("%d", &n);
printf("Enter %d real numbers\n",n);
for (i = 0; i < n; i++)
{
scanf("%f", & nums[i]);
}
for(i=0; i<n; i++)   /* Compute the sum of all elements */
{
sum = sum + nums[i];
}
mean = sum /(float) n;  /* Calculating the mean using the equation */
for(i=0; i<n; i++)  /* Compute  variance  and standard deviation */
{
v_sum= v_sum + pow((nums[i] - mean), 2);
}
var = v_sum / (float) n;   /* calculate the variance using general equation */
sd = sqrt(var);  /* calculating standard deviation */

/* prints the output mean, standard deviation, and variance */
printf("Mean of all elements  = %.2f\n", mean);
printf("The variance of all elements = %.2f\n", var);
printf("Standard deviation SD = %.2f\n", sd);
}```
```

## OUTPUT

```Enter the number of elements
6
Enter 6 real numbers
12
34
10
50
42
33
Mean of all elements  = 30.17
The variance of all elements = 215.47
Standard deviation SD = 14.68
```

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