~Write a C++ program that computes the central tendencies mean (average), mode,

Question

~Write a C++ program that computes the central tendencies mean (average), mode, median and the variation: variance, standard deviation and range for a set of numbers given in the data file ArsenicGroundWaterFile.txt.~

~The following data represent (naturally occurring) concentration of arsenic in ground water for a random sample of 102 Northwest Texas wells. Units are parts per billion.~

~The output should be as follows to two decimal places:~

Central Tendency      Variation     

Mean    xxx.xx             Variance xxx.xx

Median xxx.xx             Std. Dev xxx.xx

Mode    xxx.xx             Range     xxx.xx

__________________________________________

data in text file as follows:

Explanation / Answer

Here is the code for you:

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

double Mean(double numbers[], int count)
{
double mean = 0.0;
for(int i = 0; i < count; i++)
mean += numbers[i];
mean /= count;
return mean;
}

double StandardDeviation(double numbers[], int count)
{
double stdDev = 0;
double average = Mean(numbers, count);
for(int i = 0; i < count; i++)
stdDev += pow((numbers[i] - average), 2);   //Sum of (number - average) whole square.
stdDev = sqrt(1/(double)count * stdDev);     
return stdDev;
}

double Median(double array[], int size)
{
    int middle=0;
    double average=0, median=0;
middle = size / 2.0;   //Calculates the middle value in the array.
if (size % 2)   //If there are odd number of elements in the array.
    median = array[middle];
else   //If there are even number of elements in the array.
   median = (array[middle] + array[middle + 1]) / 2.0;
return median;
}

double Mode(double p[], int n)
{
    int counts[n];
    for(int i = 0; i < n; i++)
        counts[i] = 0;
    for(int i = 0; i < n; i++)
        counts[p[i]-1]++;
    int highestCount = 0;
    for(int i = 1; i < 9; i++)
        if(counts[i] > counts[highestCount])
            highestCount = i;
    return highestCount+1;
}

double Variance(double array[], int n)
{
double sum = 0;
double avg = Mean(array, n);
for(int i = 0; i < n; i++)
sum += pow(array[i] - avg, 2);
return sum / n;
}

int main()
{
    ifstream fin;
    fin.open("ArsenicGroundWaterFile.txt");
    double array[102];
    for(int i = 0; i < 102; i++)
        fin>>array[i];
    cout<<"Mean   "<<fixed<<setprecision(2)<<Mean(array, 102);  
    cout<<" Variance   "<<fixed<<setprecision(2)<<Variance(array, 102);  
    cout<<" Median   "<<fixed<<setprecision(2)<<Median(array, 102);  
    cout<<" Std. Dev   "<<fixed<<setprecision(2)<<StandardDeviation(array, 102);  
    cout<<" Mode   "<<fixed<<setprecision(2)<<Mode(array, 102);  
    cout<<endl;
}

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