In C programming, arithmetic mean

The arithmetic mean is the sum of a set of numbers divided by the number of numbers in the set.

Basic properties of the arithmetic mean

• n The average of the numbers x1, x2,. . .,xn is x. If each observation is increased by p, then the mean of the new observations is (x p).

• #n Numbers x1, x2, . . .,xn is x. If each observation is reduced by p, then the mean of the new observations is (x - p).

• n Numbers x1, x2, . . .,xn is x. If each observation is multiplied by a nonzero number p, the mean of the new observations is px.

• #n average of em> numbers x1, x2, . .,xn is x. If each observation is divided by a nonzero number p, the mean of the new observations is (x/p).

Arithmetic mean formula

Type 1: Direct average

Given array and number of elements

Input- 1,2,3,4,5,6,7,8,9

Output- 5

Explanation- To calculate the arithmetic mean of all numbers, first add all the numbers, then create a variable responsible for the arithmetic mean and put the addition/size into the variable like armean .

Example

#include<iostream>
using namespace std;
int main(){
   int n, i, sum=0;
   int arr[]={1,2,3,4,5,6,7,8,9};
   n=9;
   for(i=0; i<n; i++) {
      sum=sum+arr[i];
   }
   int armean=sum/n;
   cout<<"Arithmetic Mean = "<<armean;
}

Type 2: Given range and number of elements present.

Given three integers X, Y and N. Find the arithmetic mean of N between logical X and Y.

N terms in an arithmetic series (the number of terms between #- Explanation

Suppose X1

, X

2, X3

, X

4

……X

n is the arithmetic mean between N two given numbers X and Y.

Then X, X

1_{, X}2_{, X}3_{, Y will be in an arithmetic series. Now Y = the (N 2)}th term of the arithmetic series. Find the (N 2)_{th term of the arithmetic series where d is the tolerance}

X= first and
Y= last terms.

Therefore the tolerance d is given by.

22 24 26 28 30 32 34

_{We have the value of} A _{and the value of the tolerance (d), now we can find all N arithmetic means between X and Y. Example}

Y = X + (N + 2 - 1)d
Y - X = (N + 1)d

_Output

d = (Y - X) / (N + 1)

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