Exercise 3-2

/*
 * This program uses the following method for calculating quartiles:
 * http://en.wikipedia.org/wiki/Quartile#Method_1
 */

#include <algorithm>
#include <iomanip>
#include <ios>
#include <iostream>
#include <string>
#include <vector>

using std::cin;
using std::cout;
using std::endl;
using std::setprecision;
using std::sort;
using std::streamsize;
using std::string;
using std::vector;

int main()
{
    // retrieve data from user
    cout << "Enter values, followed by end-of-file: ";

    vector<double> data;
    double x;

    // invariant: data contains all the values read so far
    while (cin >> x)
    data.push_back(x);

    // check that data is not empty
    typedef vector<double>::size_type vec_sz;
    vec_sz size = data.size();
    if (size == 0) {
    cout << endl << "You must enter some values. Try again." << endl;
    return 1; // ERROR
    }

    // sort the data
    sort(data.begin(), data.end());

    /*
     * There will be mid elements in both upper and lower sublists (assuming the median is not included):
     * lower_half_size = upper_half_size = mid
     */
    vec_sz mid = size / 2;
    vec_sz lower_mid = mid / 2;
    vec_sz upper_mid;
    double median, lower_quartile, upper_quartile;

    // determine midpoints of median and upper/lower halves
    if (size % 2 == 0) {
    median = (data[mid] + data[mid-1]) / 2;
    upper_mid = 3 * mid / 2; // mid + (mid/2); median is not a datum so mid is beginning of list
    } else {
    median = data[mid];
    upper_mid = (3 * mid / 2) + 1; // median should not be included
    }

    // calculate median
    median = (size % 2 == 0) ? (data[mid] + data[mid-1]) / 2 : data[mid];

    // calculate lower and upper quartiles
    if (mid % 2 == 0) {
    lower_quartile =  (data[lower_mid] + data[lower_mid-1]) / 2;
    upper_quartile = (data[upper_mid] + data[upper_mid-1]) / 2;
    } else {
    lower_quartile = data[lower_mid];
    upper_quartile = data[upper_mid];
    }

    // write out quartiles
    streamsize prec = cout.precision();
    cout << "The quartiles are " << setprecision(3) << lower_quartile << ", " << median << ", and "
     << upper_quartile << "." << setprecision(prec) << endl;
    return 0;
}