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// Author: Anton Xue 	K26
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// finds sum, average, and standard deviation for an array of numbers entered
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/*
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Sample run:
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Enter number of elements: 6
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Enter element number 1: 9
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Enter element number 2: 2
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Enter element number 3: 4
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Enter element number 4: 5
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Enter element number 5: 7
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Enter element number 6: 12
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Total sum: 39
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Average: 6.5
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Standard deviation: 3.61939
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*/
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#include <iostream>
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#include <cmath>
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using namespace std;
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int main() {
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    // prompt user for input of number of elements and store it in a variable
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    int size;
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    cout << "Enter number of elements: ";
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    cin >> size;
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    // tell user to input that many elements and store them in an array
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    double elements [size];
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    for (int i = 0; i < size; i++) {
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        double user_input;
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        cout << "Enter element number " << (i + 1) << ": ";
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        cin >> user_input;
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        elements[i] = user_input;
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    }
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    // calculate the average of the array
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    double average;
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    double total_sum = 0;
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    for (int i = 0; i < size; i++) {
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        total_sum = total_sum + elements[i];
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    }
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    average = total_sum / size;
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    cout << "Total sum: " << total_sum << endl;
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    cout << "Average: " << average << endl;
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    // calculate the sum of each element's difference from the average squared
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    double difference_sum = 0;
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    for (int i = 0; i < size; i++) {
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        double difference_squared = pow((average - elements[i]), 2);
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        difference_sum = difference_sum + difference_squared;
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    }
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    // apply the standard deviation formula
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    double stdev = sqrt(difference_sum / (size - 1));
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    cout << "Standard deviation: " << stdev << endl;
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}