Question
The standard deviation of a list of numbers is a measure of how much the num-
bers deviate from the average. If the standard deviation is small, the numbers are
clustered close to the average. If the standard deviation is large, the numbers are
scattered far from the average. The standard deviation, S , of a list of N numbers x i
is defined as follows,
where
is
the average of the N numbers x 1 , x 2 , .... Define a function that
takes a partially filled array of numbers as its argument and returns
the standard deviation of the numbers in the partially filled array.
Since a partially filled array requires two arguments, the function
will actually have two formal parameters: an array parameter and a
formal parameter of type int that gives the number of array positions
used. The numbers in the array will be of type double . Embed your
function in a suitable test program.
Answer
PROGRAM CODE:
//Header section
#include <iostream>
#include <cmath>
using namespace std;
// Function to calculate the average of the numbers in the array
double calculateAverage(double numbers[], int size)
{
double sum = 0.0;
for (int i = 0; i < size; i++)
{
sum += numbers[i];
}
return sum / size;
}
// Function to calculate the standard deviation of the numbers in the array
double calculateStandardDeviation(double numbers[], int size)
{
double average = calculateAverage(numbers, size);
double sumOfSquares = 0.0;
for (int i = 0; i < size; i++)
{
sumOfSquares += pow(numbers[i] - average, 2);
}
double standardDeviation = sqrt(sumOfSquares / size);
return standardDeviation;
}
//Program begins with a main method
int main()
{
const int MAX_SIZE = 100;
double numbers[MAX_SIZE];
int size;
// Get the number of array positions used from the user
cout << "Enter the number of array positions used: ";
cin >> size;
// Validate the number of array positions used
if (size <= 0 || size > MAX_SIZE)
{
cout << "Invalid number of array positions used. Please enter a value between 1 and " << MAX_SIZE << endl;
return 0;
}
// Get the numbers from the user
cout << "Enter " << size << " numbers: " << endl;
for (int i = 0; i < size; i++) {
cout << "Number " << i + 1 << ": ";
cin >> numbers[i];
}
// Calculate the standard deviation of the numbers
double standardDeviation = calculateStandardDeviation(numbers, size);
// Display the standard deviation
cout << "The standard deviation of the numbers is: " << standardDeviation << endl;
return 0;
}
OUTPUT OF THE PROGRAM CODE:
Enter the number of array positions used: 5
Enter 5 numbers:
Number 1: 5.5
Number 2: 3.4
Number 3: 6
Number 4: 8.4
Number 5: 9
The standard deviation of the numbers is: 2.03529