// Author: Anton Xue    K26
// finds sum, average, and standard deviation for an array of numbers entered

/*
Sample run:

Enter number of elements: 6
Enter element number 1: 9
Enter element number 2: 2
Enter element number 3: 4
Enter element number 4: 5
Enter element number 5: 7
Enter element number 6: 12
Total sum: 39
Average: 6.5
Standard deviation: 3.61939

*/

#include <iostream>
#include <cmath>
using namespace std;

int main() {

    // prompt user for input of number of elements and store it in a variable
    int size;
    cout << "Enter number of elements: ";
    cin >> size;

    // tell user to input that many elements and store them in an array
    double elements [size];
    for (int i = 0; i < size; i++) {
        double user_input;
        cout << "Enter element number " << (i + 1) << ": ";
        cin >> user_input;
        elements[i] = user_input;
    }

    // calculate the average of the array
    double average;
    double total_sum = 0;
    for (int i = 0; i < size; i++) {
        total_sum = total_sum + elements[i];
    }
    average = total_sum / size;
    cout << "Total sum: " << total_sum << endl;
    cout << "Average: " << average << endl;

    // calculate the sum of each element's difference from the average squared
    double difference_sum = 0;
    for (int i = 0; i < size; i++) {
        double difference_squared = pow((average - elements[i]), 2);
        difference_sum = difference_sum + difference_squared;
    }

    // apply the standard deviation formula
    double stdev = sqrt(difference_sum / (size - 1));

    cout << "Standard deviation: " << stdev << endl;
}