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

Here in this C program, we need to find out Mean, Variance, and Standard deviation; we need to know what is meant by Mean, Standard deviation, and Variance.

## What is Mean?

Mean: it is the average of all elements in a set of values. Means 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.

## Explain the term 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 by taking the average of the sum by using a '`for loop`' after that, we need to calculate variance using the formula.

``````"sum1 = sum1 + pow((x[i] - avrg),2)"
var = sum1 / (float) n; ```
```

After calculating the variance, it is easy to find the standard deviation. Estimate the standard deviation of the set; we use the sd = sqrt(var) formula in this c program. Finally, we have to display the mean, variance, and standard deviation using `printf` in the c language.

### 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 used in the program.

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 zero to the number of terms to calculate the Mean.

STEP 6: Calculate Mean by finding the Sum and divide that with the number of terms.

STEP 7: Open another For loop from zero to 'n' to find the Variance.

STEP 8: Calculate the Variance using the formula sum1 = sum1 + pow((x[i] - avrg),2 and apply the sum1 in main formula var = sum1 / (float) n.

STEP 9: Calculate the Standard deviation by taking the square root of Variance.

STEP 10: print the Mean, Standard deviation, and Variance using `printf` built-in functions in C.

## C Source Code

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

void main()
{

float x[MAXSIZE];
int  i, n;
float avrg, var, SD, sum=0, sum1=0;   /* declares the variables avrg, Sd, sum as float */
printf("Enter the value of N\n");                  /* accepts values from user */
scanf("%d", &n);
printf("Enter %d real numbers\n",n);
for (i = 0; i < n; i++)
{
scanf("%f", &x[i]);
}
for(i=0; i<n; i++)                                        /* Compute the sum of all elements */
{
sum = sum + x[i];                                     /* calculating the mean using the equation */
}
avrg = sum /(float) n;
for(i=0; i<n; i++)                                 /* Compute  variance  and standard deviation */
{
sum1 = sum1 + pow((x[i] - avrg), 2);    /* calculate the variance using general equation */

}
var = sum1 / (float) n;
SD = sqrt(var);                                                      /* calculating standard deviation */
printf("Average of all elements  = %.2f\n", avrg);
printf("Varience of all elements = %.2f\n", var);
printf("Standard deviation SD = %.2f\n", SD);               /* prints the output mean, standard deviation, and variance */
}```
```

## OUTPUT

```Enter the value of N

6

Enter 6 real numbers

12

34

10

50

42

33

Average of all elements  = 30.17

Varience of all elements = 215.47

Standard deviation SD = 14.68```
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