Question

Write a program that calculates mean and standard deviation for four user entered values. The most common measures of a sample are the mean and the standard deviation. the mean is the sum of the values divided by the number of elements in the data set. The dispersion - or spread in the values - is measured by the standard deviation The equation for the mean is x¯ = x1 + x2 + · · · + xn The equation for the standard deviation is sx = √ (x1 − x¯) 2 + (x2 − x¯) 2 + · · · + (xn − x¯) 2 n − 1 Your program will have the user enter four values (all doubles), You might call them x1, x2,x3,and x4. The program will then pass these four values to a function called mean that will calculate and return the mean of the four values. The mean and the four values will then be passed to a second function called stdev which will calculate and return the standard deviation of the four values. You program should be using functions. There will be a function printHeader that prints the splash screen, a function mean that calculates the mean, a function stdev that calculates the standard deviation, and a function printResults that prints the four values, their mean, and their standard deviation Your program must also include comments with your name, the date, and a short description of the project. It must also print this information as a splash screen at the beginning of the program run. It should print like:

X: 4.00, 7.00, 1.00, 10.00

Mean: 5.50

Std Dev: 3.87

This needs to be done in C++. Below is the format:

//
//   Name
// 1 October 2020
//   Program to calculate the mean and standard deviation
//

//   Pound includes - will need the string and cmath libraries
#include<iostream>
#include<iomanip>
#include<cmath>
#include<string>

using namespace std;

//   Function Prototypes - Need to add three more. One for mean, one for
// standard deviation, and one for the printResults
void printHeader(string, string);
int main(void) {

   // Splash Screen
   printHeader("1 October 2020", "Calculating Statistics");
  
   //   Declare and Initialize all of the variables
   //   Will need doubles for the four data points, as well as a double
// for the mean and one for the standard deviation
  
  
   //   Prompt for entering data - you must enter four values
  
  
   // Pass the four data variables to a function that returns the mean
  
  
  
   //   Pass the four data variables and the mean to a function that returns
// the standard deviation
  
  
  
  
   //   Print the results
   //   Include the original values and the mean and the standard
// DO NOT PRINT IT HERE - pass the variables to a printResults function
  
  
  
  
  
  
  
   return 0;
}

//   Function Definitions
void printHeader(string dueDate, string description) {
//   PRINTHEADER void printHeader(string, string) prints the splash screen
//   using the two strings that are passed to the function from the driver.
//  
//   Name:   
//   Date:
//
  
   //   Print the splash screen
   cout << endl;
   cout << "Your Name Here" << endl;
   cout << "CMPSC 101" << endl;
   cout << dueDate << endl;
   cout << description << endl;
   cout << endl;

   return;
}

Answer 1

Here is the code:

//  Name
//  1 October 2020
//  Program to calculate the mean and standard deviation

//   Pound includes - will need the string and cmath libraries
#include<iostream>
#include<iomanip>
#include<cmath>
#include<string>
  
using namespace std;

//   Function Prototypes 
double mean(double arr[], int n);
double stdev(double arr[], int n);
void printHeader(string, string);
void printResults(double arr[], int n, double mean, double sd);
 
int main () 
{
    // Splash Screen
    printHeader ("1 October 2020", "Calculating Statistics");
    
    // variables initialization
    int n;
    cout << endl << "Enter the no. of elements: ";
    cin >> n;
    
    // double array
    double arr[n];
    
    // Getting elements for array
    for (int i = 0; i < n; i++) {
        cout << endl << "Enter element " << i+1 << ": ";
        cin >> arr[i];
    }
    
    // mean
    double cMean = mean(arr, n);
    // standard deviation
    double sd = stdev(arr, n);
    
    printResults(arr, n, cMean, sd);
    
    return 0;
}

//   Function Definitions
void printHeader (string dueDate, string description) 
{
    //   Print the splash screen
    cout << endl;
    cout << "Your Name Here" << endl;
    cout << "CMPSC 101" << endl;
    cout << dueDate << endl;
    cout << description << endl;
    cout << endl;
    
    return;
}

// Calculates the mean of given array
double mean(double arr[], int n) 
{
    double sum = 0;
    
    for (int i = 0; i < n; i++)
        sum += arr[i];
 
    return (sum / n);
}

// Calculates standard deviation of array and return it
double stdev(double arr[], int n) {
    // calculating mean
    double calculatedMean = mean(arr, n);

    double temp = 0;
    // Calculating variance
    for(int i = 0; i < n; i++)
    {
        temp += pow(arr[i] - calculatedMean, 2) ;
    }

    double var = temp / n;
    
    return sqrt(var); // Standard deviation
}

// Print the results (mean, standard deviation) with array
void printResults(double arr[], int n, double mean, double sd) {
    // Printing array
    cout << endl << "X: ";
    for  (int i = 0; i < n; i++) {
        cout << arr[i];
        
        // Printing commas accordingly
        if (i < n-1) {
            cout << ", ";
        }
    }
    
    // Printing mean and standard deviation
    cout << endl << "Mean: " << mean;
    cout << endl << "Standard Deviation: " << sd;
}

Output:

Your Name Here
CMPSC 101
1 October 2020
Calculating Statistics

Enter the no. of elements: 4

Enter element 1: 4

Enter element 2: 7

Enter element 3: 1

Enter element 4: 10

X: 4, 7, 1, 10
Mean: 5.5
Standard Deviation: 3.3541

Screenshot: